There are a few quirks to AirBART that I've seen confuse many, many travelers.
The AirBART bus driver will not accept cash (except from seniors), so you have to buy a ticket from one of the often-broken vending machines (located just inside the terminal and at the stop, which is on the median). The machines no longer accept quarters, do not provide change, and the ones outside are inexplicably labeled with the universal symbol for "Parking," but at least they do take credit cards. There is also a change machine that provides dollar coins inside the terminal.
Going from BART to the airport, you will need to give the driver a normal BART ticket with exactly $2 on it. Avoid missing the bus, and more malfunctioning ticket machines at Coliseum BART, by purchasing this ticket at the Powell St. station.
One last hint: AirBART busses will often pick passangers up at T1 (JetBlue's terminal) and then wait at the T2 stop for several minutes before departing for Coliseum BART. If you don't mind a short walk, and you see a bus sitting at T2, you can save 15-20 minutes by catching it there.
That's probably too much information