Biking and BARTing are two great things that don't go great together. If you wanna get people pissed off at each other, stick them in a small, crowded moving space together while one (or more) of them is holding an unwieldy object on wheels. Up the ante by having this happen during commute hours – right after the restricted bike hours end, of course – and you've got a really ugly situation.
I've learned that the best option for me is to keep my bicycle at the BART station to avoid all that. But that means leaving my house an hour earlier than I normally would in order to secure bike parking. And sometimes, even when I'm really early, there still aren't any spots available. Well shit. I hope BART adds more BikeLink lockers/rooms and in-station bike parking soon. Please don't make me buy a folding bike or a unicycle.
The good news is that it seems like BART is trying to figure out ways to make commuting for cyclists a little less painful. Last August, they tried a pilot program that allowed people to bring their bikes on BART all day on Fridays. And from March 18-22, they'll be trying a new test, to allow non-restricted bike access (in all about the first three cars) on BART for an entire week. I'm happy for all the experimenting, but I'm also hopeful for better solutions. Is it asking too much for a bike train, a la Caltrain? God I hope not.
While daydreaming on Google, I came across a few bike-meets-train solutions that actually exist and could make commuting less sucky:

Photo by georad
Caltrain has two, count 'em, two types of trains that allow for bikes: The gallery train fits 80 bikes total and the snazzily-named Bombardier allows for 48 bikes. There are bungee cords to keep your ride in place, and even seats for cyclists to take a load off during the commute.
Photo via MBTA
Boston gets a lot of shit for being ... Boston. But the MBTA has one thing that's superior to us that you can't knock: a special high-capacity bike coach. It seems like the coach only operates on one line, and for only certain parts of the year, but hey, that's one more bike train than BART has.
Photo by mtaphotos
Being a short person with the upper body strength of Steve Urkel makes me a little hesitant to suggest hanging bike racks, but I see the benefits of getting bicycles upright and out of the way. The Metro-North Railroad tested bike hooks on the M-7 and M-8 railcars. Unfortunately, they installed these hooks in the disabled section of their trains, and non-folding bicycles were still not restricted during high-commute hours. Still, the idea could be cool. I imagine these working best in a car filled with a row of these hooks, without any seating below – because getting conked in the head with a bike sounds like the worst way to start my morning.

Photo via www.stuttgart.de
Finally ... why not take a cue from the Germans and create a train with front-loading bike storage. The Stuttgart to Degerloch Zahnradbahn is an open car meant only for bicycles. It's kinda like a bigger, better, roll-on version of the bike-rack on Muni. The only thing I'd suggest is a valet to prevent theft, which I could see being a problem here.