In my state (NH), the DUI statute definitely applies to bicycle riders as a bicycle is defined as a vehicle, and DUI is is defined by statute as operating a vehicle on a way while intoxicated. Open container law, however, only applies to "motor vehicles", so they can't get you for beer in the bottle cage.

A quick look at Michigan law makes it appear that OWI laws don't apply to bicyclists. The bike statute defines a bike as a "device", not a vehicle, but states that the operator of the device has all of the same duties as a driver of a vehicle "except as to the provisions which by their nature do not have application." Exclusively human-powered devices are specifically defined out of the category of vehicles. The OWI statute definitely identifies the offense as operating a vehicle while intoxicated, which by definition a bicyclist cannot do as the bicycle is not a vehicle. Open container laws likewise apply only to "vehicles".

Might have been able to get him for drunken disorderly in Michigan if his riding appeared sufficiently impaired that he put someone or something at risk: "A person who is intoxicated in a public place and who is either endangering directly the safety of another person or of property or is acting in a manner that causes a public disturbance." That's a crime. They could also take him into protective custody (non-criminal) if he's drunk. If they want to be jerks about it, I think they could get him for the drunken disorderly for endangering the safety of his own bicycle if he had tested sufficiently intoxicated (statute doesn't specify it has to be someone else's property).