here in florida, although a bike is a vehicle under the road laws, you cannot get a DUI cycling when drunk because as you need no license to cycle, you have not given presumed consent to be breathalyzed - acceptance of a driving license is the acceptance of consent to be breathalyzed and so even if you drive a car and have a valid drivers license, you cannot lose it as there would then be different penalties for car driving cyclists and non car driving cyclists, so the ruling is no DUI for cyclists as not licensed and therefore have not consented to be tested.
But you don't need to be breathalyzed to be arrested for DUI. In many states you may refuse the breathalyzer, but you can still be arrested based on officer observation, smell of alcohol, field sobriety tests, etc.

Where I work there is definitely a contingent of low-income cyclists that don't have cars, as well as several homeless people who ride their bikes around town looking for empty bottles (for the 5cent refund), spare change, and discarded food. It really never occured to me that any of them were using bikes due to DUIs. I guess it makes sense that a certain percentage of cyclists would be using a bike due to having lost their license, but I was never aware of such a stereotype or stigma. Maybe I'm just naive.

I just wish that they would all wear helmets, whatever their reasons for being on a bike . . .