Can you loose a car licence for being drunk on a bicycle?

You can be charged with being drunk while riding a bike because you are considered a danger to yourself and to others, but you won't lose your driving license.

You can also be arrested for being drunk in charge of a vehicle even if you are not driving at the time.

In some states you can ONLY if you have upgraded the bicycle to a motorized one. The loss/suspension of a license is,generally, only applicable to a "motorized" mode of transportation.