Generally, restrictions on cars make public transport better automatically, as they make buses work better.
Not really. Unless the restriction is to take a generic lane and dedicate it to buses. But if restriction is to take a generic lane and give it to bicycles, then both cars and buses sit in the same traffic jam.
It certainly helps the buses move more efficiently, but it can't do much about things like bus stop placement, or just generally sense of place as you start or end your trip.