Since you got a DWI your best bet will be trying to prove you were on a bicycle at the time, and not driving a motor vehicle.
In Texas gas powered motor bicycles are basically illegal, but there's a loophole. In Texas all motor vehicles are considered self propelled. The police have to prove your motor bicycle is in fact self propelled. As long as you pedal away from every stop you can claim since you have to pedal to get going it's not self propelled, therefore it's a bicycle, not a motor vehicle. If you rode away from your last stop like a motorcycle without pedaling, and the police saw you do it, you're screwed. If they didn't see you, you have a chance.
I don't think you can get a DWI when on foot, or riding a bicycle, but they can give you a DUI.