I saw the water in my canteen ripple with their every step.
The adult male lowered its head and stared right through the windscreen at me.
It grunted — a giant, glassrattling snort. My heart in my mouth, I lifted my camera and gingerly pressed the button.
OK, fine. I wasn't actually in Jurassic Park and these weren't T-Rexes, they were bison. (Big, scary bison, mind. If their diet wasn't exclusively composed of grasses, sedge and other low-lying plant life, they probably would've eaten me.) But while I might have missed out on seeing any of your actual Tyrannosaurs by 65million years or so, I was right in the middle of their old stomping ground.
The Western United States is full of dinosaurs — absolutely chocka with them. The only drawback for those seeking a real-life Jurassic Park experience is that they're all dead.
But even though nobody's done a John Hammond and brought dinosaurs back from extinction — yet — at the Museum Of The Rockies in Bozeman, Montana, they've come pretty close.
If you love dinosaurs even half as much as I do, you have to visit the Museum Of The Rockies.
It's got one of the best collections of dinosaurs on the planet.
And it's run by Jack Horner — the man who changed the way the world thinks about these prehistoric creatures and who helped inspire Michael Crichton to write the original Jurassic Park book.
Jack was one of the first palaeontologists to realise that dinosaurs were related to birds.
He discovered a Maiasaura nesting site in Montana that proved the fearsome-looking beasts were actually loving parents.
And he's currently rooting through the genetic code of chickens to see if he can find enough scraps of dino DNA to hatch a real-life dinosaur from an egg.
I was lucky enough to be shown around the museum by Jack himself — a wry, silver-haired Montanan who seems always to be carrying a pickaxe — but even though he isn't around on a day-to-day basis, he's recorded an audio tour that will introduce you to all of the museum's residents, including "Big Mike", a 38ft Rex discovered up the road in Hell Creek.
Seeing these fossilised monsters face to face is awe-inspiring — even more so when you realise that back in the Cretaceous period, the things would've been lumbering around the car park.
Although Bozeman is in the middle of nowhere, it is surprisingly easy to get to. I flew there from Chicago in three hours for £180 return and there are regular flights from many major US cities — so making a detour on holiday in the States is simple.
I stayed at the town's Hilton Garden Inn — a clean, cheerful and family-friendly hotel which serves delicious, T-Rex-sized portions of pancakes and bacon for breakfast, slathered in maple syrup.