Not on my bike, but on my horse I have seen multiple instances of interesting behaviour of ordinary and even rare wildlife as the wildlife concerned very often only notice the horse and not the human on top of it, and they usually aren't the least bit bothered about the presence of a horse.
Many years ago, when osprey were only just returning to Scotland, I was riding along a track by a reservoir in the Peak District in the early morning when I saw a splash and a flash of black and white - then a big bird sat in a tree, tearing and munching at a big fish. An osprey on its way back up to Scotland! When I mentioned what I thought I'd seen at a lunchtime stop in a local pub, the barman 'hushed' me then looked around carefully before leaning across the bar and saying 'we know, but we don't talk about except to the RSPB ranger ... you're the first one this year to report it so I'll give him a ring later. Please don't chat casually about it is all he asks.'