Have you ever been on a bus when it gets to use the bus lane? Bus lanes let buses skip past car traffic... so they do speed things up for people riding them. If buses had to sit in every car jam, trips would take way longer. Sure, sometimes buses still get stuck, but overall, the lanes make a big difference. Without them, bus schedules would be a mess during rush hour.
Oh man, I saw a study about this last year. They tracked buses in a few cities and the time saved with dedicated lanes was huge, like 20% faster trips on some routes. It really does add up over a week for regular riders. That extra time means drivers can actually keep closer to the schedule. It's one of those simple things that just works when people follow the rules.