Bicycles are defined as vehicles. Two vehicles may not occupy the lane, side by side (Georgia exception: two bicycles). Vehicles are required to safely pass in the left hand lane, obeying all lane markings and traffic signs (Georgia exception: vehicle may cross double yellow, to pass bicycle when safe to do so) .
Imo, unprotected bike lanes and 3ft rules are red herrings.... Just enforce the above rules! Vehicle operators tend to act one way around larger slow vehicles, and differently around bicycles...