Well, not reeaally public transportation as such, but the best story has to be the drunk elderly lady on the airport authority parking-lot bus.
This was in the dead of winter, and so the bus driver took pity on the passengers and decided he would take us all right to our cars, rather than the lot's designated stops, so he started to drive up and down each row, and asked us all where we were parked. One of the passengers was a very prim-looking older lady who was traveling alone, except that she was accompanied by a pet cat in a carrier. When the driver asked where she was parked, she started wondering aloud where that might have been, and it rather quickly became apparent that not only did she have no idea where her car was, she was also very drunk. At first she was just kind of dithery, but then the situation descended into full farce when she decided that the cat probably knew where the car was, if only he would just TELL her, so we drove around the lot for 20 minutes while she interrogated the cat. "Kitty, where did I leave the car?" "Come on, it's cold outside; you have to tell me where it is." "Is it this row, Kitty?" She was still at it when DH & I got off at our car.
It happened over 20 years ago, but to this day I hope that the cat stayed mum, so that she stayed on the bus long enough to sober up before driving home.