When I've cycled to work and gone for drinks afterwards, I'll leave my bike at the office and pick it up the next day, using public transport to get there.
The good thing is, "too drunk to ride a bike" happens much earlier than "too drunk". And while with a car some push it and still drive drunk (sometimes with horrendous consequences), a bike has this safety mechanism where they simply cannot be ridden when drunk.
I am a practiced cyclist and an accomplished drinker, and I can tell you that I am able to operate a bicycle deeper into intoxication than I can reliably walk.
It's as if all bikes came with their own tamper proof drunk driver detector and drunk usage preventer: a built-in continuous driver balance testing system, even more reliable than a breathalyzer, and able to detect all kinds of other drugs too.
Drunk tricycle driving and bikes with training wheels: now those much more inherently dangerous problems!