It had been a long drive: back roads and dirt trails, the ruins of grand haciendas and overgrown sisal plantations, villages of huts huddled around bone-white fortified churches. We got lost several times and our Spanish flummoxed the locals – if we could find anyone. Most were inside, snoozing in hammocks. The light turned golden and the heat was fuddled by dust. There were men on motorbikes carrying crude wooden cages filled with wild birds – red cardinals to sell in the towns – and there were flowering trees galore. I really could not see, however, how this place was going to be what had been promised: a world biodiversity hotspot. We were not in an Attenborough documentary at all, this was a Dylan song, with its cast of renegade priests, Mexican bandidos and doomed lovers.

"Will we see dolphins before dark?" Maddy (eight) asked. Then, "Can we swim with them? You said this was where loads of animals and birds live, but I can't see any." Life, someone once said to me, is about managing expectations. Travel and parenting, I could add, certainly are.

We were approaching Celestún in Mexico, one of the precious zones of the globe where nature has spawned species with outrageous fecund glee: 17,000 vascular plants, 440 mammals, 500 freshwater fish, 1,240 reptiles and amphibians, and more than 1,120 birds. This is only one of 25 places in the world where nature went on an evolutionary rampage, spinning extraordinary numbers of species in a small area, according to scientists. The Mesoamerican hotspot straddles the isthmus and includes our location, Celestún biosphere reserve on the western coast of Mexico's Yucatán peninsula. That this area is home to a staggering range of species is all the more remarkable because it is also a place that was once devastated by human greed.

In the mid-19th century, the majority of the Yucatán's rich forests were felled to make way for sisal plantations, a crop that produced fibre for gunny sacks. Sisal boomed. Fortunes were made, vast estates built up, a whole feudal Hispanic culture evolved. Then, with rising foreign competition and some serious revolts by the Mayan population, it was over. Plantations were abandoned and became overgrown. Birds and wildlife returned. Or so we had been led to believe.

As the sun dipped and approached the horizon, we raced to the hotel and exploded out of the car desperate for a swim before nightfall, nodding briefly at the receptionist – "Back in a minute" – and ran to the ocean. We were absolutely alone, with the sun poised momentarily on the horizon. Maddy and I ran into the tranquil water, but my partner Sophie stayed on the beach. There was no one around, no one to pick up all the shells. We were waist-deep, splashing madly and Sophie was jumping up and down, waving her arms. I waved back. Sophie waved harder. She was mouthing something. I laughed and splashed Maddy. With the waves I couldn't make out what Sophie was saying. Why was she jumping up and down? And now she was shouting, very loudly and pointing, "KEVIN! BIG FISH!"

I turned and saw the fin cruising behind me, only a few metres away. I turned back and grabbed Maddy, heaving her up out of the waist-deep water. "Beach time."

My heart was thumping. Maddy wriggled and fought. "No! I don't want to." Then she saw the fin too, and the other one, now a stone's throw away. She went still.

"Are they really sharks, Daddy?"

And despite my adrenaline surge, I noticed the shape of the fin and the way it cut the water. I sighed. We had scared them and they were far away now.

"Dolphins."

I set her down in the water and lost sight of them. Had they dived? It was too dark to tell. I felt a pang of regret: what we had wanted was right under our noses and we had failed to see it.

Hotel Ecoparaíso

When you cannot see what is right in front of you it is time to get a guide to point it out. We asked at our hotel, the idiosyncratic and wonderfully remote Ecoparaíso, and they said: "A wildlife guide? Alex Dzib. He's the best. Lives down near the town of Celestún." We rang him up and booked him.

The next day we spent beach-combing. There were no other guests at Ecoparaíso – a perplexing fact since it seemed to be a fabulous place. Jaime Garza, the manager was rueful: "Our clientele is mainly American and they have temporarily deserted Mexico because of the drugs wars. Not that we see any sign of those problems here." It seemed painfully ironic that drug wars caused Americans to turn their noses up at Mexico, the same noses where all the drugs go.

For Ecoparaíso it is a great shame since this hotel manages to be both luxurious and genuinely green, a difficult trick to achieve. They were keen to show me where the poo went, a vital part of the equation since a change in the water table can be disastrous for this coastal ecosystem. We made use of the solar-heated pool and admired the resident iguanas. Although the building of the hotel inside a biosphere reserve aroused much controversy, the result is that many birds have found a safe home within its grounds: safety from poachers who hunt the more colourful specimens and take them off to market for sale.

Next morning at dawn we were in a dry forest a few miles away with Alex. He is short and rotund and very jovial – a sort of Mexican Bill Oddie – who entertained Maddy relentlessly. The dawn was hazy and Alex kept apologising for absent friends between a barrage of whistles, hoots, trills and caws. Alex could do every bird we couldn't see. "We should spot the ferruginous pygmy owl – imagine an owl the size of a tennis ball … but he's not here."

Looking down at the patch of mud, Alex grinned. "Hey, look at this!" He was squatting down, pointing to some tracks, "Opossum prints."

We gather around, dutifully interested. "I know," admitted Alex, "the opossum is not here either – but we're still early." The early morning air was heavy, and nothing, apart from ourselves, moved. A few half-remembered lines of Henry Reed's second world war poem Naming of Parts ran through my head: "Today we have naming of parts … which in our case we have not got." I was tempted to enquire if all the much-vaunted species had stayed away along with the American tourists.

Then, just as the sun finally tore aside the curtains of mist, things burst into life. "Altamira oriole, ladder-backed woodpecker, vermilion flycatcher, Carnivet's emerald hummingbird, turquoise-browed motmot … " The pace of birds became surprising, then astonishing, then ridiculous. I couldn't write the names down fast enough. "Don't worry, we'll go through them in the book later."

Our guide Alex on boardwalk. Photograph: Kevin Rushby/The Guardian

Alex was chucking his spotting scope around like a gunfighter wields a Colt 45. He'd see the bird before it moved and have that scope on it in milliseconds, ready for us lesser mortals. The man was a prodigy. "My father was a fisherman who knew a bit about birds here – before anyone came looking for them. Then a National Geographic film crew turned up. They'd heard it was an amazing birding spot and they needed a local guide. I was a kid and I went along." Alex never looked back. If there was a world title for bird guide, I'd award it to him. Between spotting new species, he was keeping Maddy riveted with tales of unbelievably nasty insects. Her favourite was the ichneumon wasp that lays an egg in your arm, which then hatches, digs deeper, pupates and sends up a breathing hole. The only way to get it out, Alex assured her, is to tie a piece of fresh meat over the hole and tempt it out. "Does it hurt?" asked Maddy.

He showed her a scar on his arm. "It did last time I had one."

And then, Alex gave a little whistle of delight and thrust my head to the scope in time to spot a bundle of feathers: the ferruginous pygmy owl, or as I preferred, tennis ball owl, staring directly back at me.

After that excitement we headed back to the town of Celestún and jumped aboard a boat, cruising across the bay spotting dolphins – easy when you have Alex on board to point out that they are often found under the soaring shapes of frigate birds. We were aiming for the one bird sight that all tourists here never miss: the flamingos. You don't need a bird guide to spot them – there are tens of thousands – but after we had enjoyed the sight of so many pink, long-legged creatures, we were landing at a small wooden quayside. "Hammock forest," announced Alex. "This is special. Go slowly and quietly."

A hooded oriole, Yucatán, Mexico. Photograph: Kevin Rushby for the Guardian

The boardwalk led us deeper into the flooded forest. Huge fish, tarpons, basked in the shallows. A bare-throated tiger heron stood motionless a few metres away. An American pygmy kingfisher perched within touching distance, its eyes sparkling in a shaft of sunshine. We watched it for a long time and then, with a brief whirr of wings, it was gone. A shadow briefly passed across me and I glanced up in time to catch sight of an osprey gliding overhead. "85% of our ospreys are migratory," whispered Alex. Apart from anecdotes, scary stories and sheer, unadulterated enthusiasm, he could also marshall an impressive battery of statistics. "That was a female – 60% of our ospreys are female."

Back at the dock we said goodbye, reluctantly, to Alex. I still had the feeling we were wandering through a Dylan song, but there was a new character to add to Bob's usual repertoire of Mexican desperadoes and renegade priests: the hotshot birdwatching guide.