You can go your entire private pilot career and never fly in Class B airspace. Often it is by choice. There are pilots who eschew controlled airspace of any kind and will take a zigzag route on a cross-country flight to avoid having to talk to a control tower for a transition.
Recently I met a man with a pilot certificate who asked if he would need special training and an endorsement to fly solo through Bravo. Not if he held private pilot certification. I suppose the FAA figures if you have earned a private pilot certificate, you have learned how to talk to a control tower, get a discreet squawk code, and follow directions.
