more specific..not because of having a PPL or not, but obtain ATC clearance and aircraft must be equipped with a two-way radio for communications with ATC and an operating Mode C transponder, furthermore aircraft overflying the upper limit of any Class B airspace must have an operating Mode C transponder.
Visual Flight Rules (VFR) flights may proceed under their own navigation after obtaining clearance but must obey any explicit instructions given by ATC.
Pilots operating in Class B airspace must have a private pilot's certificate, or have met the requirement of CFR 61.95. These are often interpreted to mean "have an instructor's endorsement for having been properly trained in that specific Class B space." However, it does not apply to student pilots seeking sport or recreational certificates. Some Class B airports (within Class B airspaces) prohibit student pilots from taking off and landing there and are listed in the AIM .