There are several streets in Madison with
contra-flow bike lanes. Most are not physically separated unlike the one on University. It can and does work very well when the contra-flow travel was well thought out. On a low traffic one way street, it can be a real godsend. And it's not like downtown has a shortage of those...
There are also contra-flow areas that work very very badly. One of the streets that pairs with University for car traffic has a contra flow lane that is not separated. At least I *think* it's a contra flow lane. The markings are unclear, and it doesn't make a whole lot of sense to have bike lanes on both sides of a one way street that are both in normal travel direction. The standard Madison bike lane marker is a simple diamond, so it doesn't provide directional cues. And no median strip means it is legal for a left turning vehicle to take the lane (this is due to some oddities intended to minimize right hooks - a driver making a turn is supposed to get as close to the curb as practicable).
If Madison were consistent and had a flat rule that all streets are two way for bikes, the grid would be more comprehensible. Right now, most cyclists can figure out University, but other contra-flow lanes can be a great place to people watch to see how understandable a facility is. Often, the answer is "not very". The contra-flow bike lane through Villas Park is a great example. You'll see joggers, wrong way cyclists, pedestrians, kids playing chicken, and a lot of frustrated cyclists going the right direction. You'll also see wrong way cyclists in the main travel lane on occasion.
Given the high confusion factor of a contra-flow bike lane, I'm not a huge fan. It's taken decades for there to be a large enough pool of cyclists that the University contra-flow lane works *well*.