The bike lane should be on the uphill side. The problem is that passing on an uphill is significantly less safe than on a downhill because the driver typically can't see oncoming traffic. The most dangerous scenario is the passing driver swerving back suddenly to avoid an oncoming car and hitting the cyclist. Passing is less likely to occur on the downhill, but it's also going to tend to be safer as the driver can see traffic in the oncoming lane.
Bonus: if a lane is to be shared, it should be as narrow as possible. Wider lanes encourage drives to try to squeeze past a cyclist when there is no room to safely pass. Wider lanes also encourage higher speeds. There is never a benefit to the cyclist. The only good reason for wider lanes is for large trucks. I think it's reasonable in industrial areas, for example, where large trucks are common. I don't think it's reasonable in residential or commercial districts.
Bonus: if a lane is to be shared, it should be as narrow as possible. Wider lanes encourage drives to try to squeeze past a cyclist when there is no room to safely pass. Wider lanes also encourage higher speeds. There is never a benefit to the cyclist. The only good reason for wider lanes is for large trucks. I think it's reasonable in industrial areas, for example, where large trucks are common. I don't think it's reasonable in residential or commercial districts.