Many BART elevators are broken, and many more are kept locked or turned off, ostensibly to prevent vandalism but also to make it more difficult for the handicapped and bike riders to move about.
Do not try to get your bike through a turnstile unless you are very fast. Instead, leave it on the other side of the waist-high "fence" and move through yourself, then lift it over to you.
There are times (during rush hour) that you may not take your bike on BART. Even during rush hour, you may bring it on at the San Francisco Embarcadero station for transbay travel.
Many AC Transit busses are equipped with bike racks. The lines that run all night (e.g., 40 and 51) all have bike racks, as far as I understand. Space enough for two bikes exists on the standard racks. One must lift the bike onto the rack with the front wheel facing toward the "hook." Then the hook must be pulled all the way over the front wheel of the bike.
It is conventional for the rider of the last bike off the rack to put the rack back up. There is a catch in the middle of the front of the rack that must be pulled to release the whole rack structure, which is then pushed up against the grille of the bus.
If any part of this is omitted or performed in an abnormal fashion, the bus driver will often honk the horn, gesticulate and mouth inaudible words through the windshield.
Any info on MUNI, Amtrak, etc., would of course be appropriate here.