I primarily shoot take-downs, no matter what. But when I go out on my mountain bike, I leave the bow put together. That being said, this year I may start taking it down, since I am shooting a BW longbow that comes apart and goes back together in seconds.
I used to ride with a setup like 'elknutz' has above, but was nervous about what could happen to my bow if I ever wiped out. (I ride both before and after daylight hours, with a light, quite a bit when hunting.) So I sewed some elastic straps to carry my bow on my hunting backpack. It works great!