The 7am southbound bullet used to be really hard to get a spot on since there are only 16 bikes allowed in a bike car and usually only one bike car per train. After the schedule change, it's a little easier to get on there, but I haven't ridden caltrain since december, so...
1976 schwinn paramount P 14, 80s casati road bike, and 60s mercier fixed conversion
there was one time it had 2 car trains. it was actually on the way back from NAHBS. north end bike car was already filled but there luckily was another one on south end. not sure if caltrain had made a special arrangement that day in anticipation of more riders with bicycles or not but it sure was nice as i didn't have to wait another hour.
i occassionally go down to san jose (company HQ is there) and i have ridden bullet trains with my bike and never had any issues with it, but that might be because i'm usually at the station 5-10 minutes before the train leaves.
I've been turned away from a 8:00 southbound bullet, as Judah said, because there was only one bike car on a new-style train with 16 spots. I get on the train at 22nd street, and the car had already filled with bikes at 4th and King. Other than that one time, I bring my bike on every day from SF to mountain view and back with no problems.
As a side note, it makes for a nice ride to just jump off the train a little early.