The bus ride is 5-10 minutes. I've never waited more than 15 minutes.
After you exit the terminal at SFO, you'll have to take the train to the
Bart station. I think it's 1 stop if you're on UA. After you exit, you'll see the BART ticket machines. I hate those machines.

If I recall, they don't accept AMEX. Also, IIRC, you have to put your credit card in the machine differently than you normally do.
I now buy a card with additional fare loaded so that I can avoid those dreadful machines. They're not friendly to the 3x a year user.
Dan