Dunno how it is in US but where I am from you can certainly lose your rights to ride a bike. You do jot need driving license for it ofc. But if you got caught dui in a car, you’d be losing rights to any forms of personal transportation including bike. Pretty sure if you get caught driving bike dui, you’d be losing driving license for a car too.

I mean, nobody would stop you from riding bike. But riding it drunk or high would lead you to fines and restrictions for sure.