Yeah, but biking is under your own power.
I didn't, by the way - catch a bus. Biked the whole way there and back, nice long loop. 70ish minutes of biking which is more exercise in one stretch than I've done in a while.
Don't underestimate how tiring it can be to ride a horse! A lot of muscles are at work, and I bet after a 70 minute horseback ride you'd feel it even more than biking.... I think it's hard not because it's particularly calorie burning, but because the muscles in your legs and back are needing to be flexed without being able to move and stretch much. You get really stiff.