BART departs more frequently, but not as reliably. You can set your watch by Caltrain. Unfortunately for you you are taking it on the weekend, on weekdays Caltrain has 5 departures an hour during rush hour and service on the half hour off peak, and most of the trains are some form of bullet train. I can get from Mountain View to downtown SF in 44 minutes, BART from *Millbrae* to Embarcadero takes 35.
Join the chorus asking Caltrain to expand weekend service, by using Caltrain on the weekend. BART can't really expand service any more without huge outlays, Caltrain can.
And you can save time by eating your breakfast on Caltrain, snack on a powerbar on BART and you risk a $250 ticket.
Your monetary comparison is completely skewed. $8 Round trip Millbrae to Embarcadero, plus $10 in gas round trip, at least. If you were driving to Lawrence for Caltrain you could have just driven to Sunnyvale, had one less zone, and the day pass would have been $11.50.
A lot of people complain that we need more capacity for bikes on Caltrain, I agree, but Caltrain has done pretty well by bikers. BART on the other hand definitely treats us as a pain in the ass they sort of deal with.