Edit: Also Google Maps says San Rafael to Palo Alto will take 2 hours give or take a few minutes on public transit, with 3 buses, but the middle one you could easily cut out with a bike or a 4 block walk. That doesn't really seem absurd at all for an occasional trip. People do 2 hour drives for an occasional trip and no one bats an eye.
This is just wrong. FWIW, I owned a bike, and this is wrong under both "bike" and "non-bike" conditions.
If you live directly next to the San Rafael central station, that'd be easiest/fastest. But San Rafael is much bigger than that. I'll get into that in a second. There are 2 basic options to do this trip:
Fastest option 1 was to go to San Rafael Station (I'll call it SR here on out) then bus to SF, then bike/walk to the Caltrain station, which was about a 25 minute walk. The buses from SR to SF ran often as rarely as once per hour, and occasionally they just don't show up at all. The ride took 30-60 minutes depending on traffic. There weren't always bike spaces on the bus, so sometimes you needed to lock your bike up in SR and you were going to be walking in SF to Caltrain. But because of the variability on traffic times, you have to leave incredibly early if you want to catch the fastest train to Palo Alto. And if you're going to California Avenue (which was where I was going to), the express option basically doesn't exist.
Here's how that plays out: 10 minute bike to SR station (or 30-40 minute walk, depending on your walk speed), you have hopefully timed things right to get on a bus leaving once every 30-60 minutes and that the bus is actually showing up: otherwise, you're waiting 30-60 minutes for the next one. Then a 30-60 minute ride into SF. Then a ~5 minute bike ride or 15-20 minute walk to Caltrain. Then a 45-60 minute ride to Palo Alto, but again the transfers aren't timed (they couldn't be, given the difference of where the bus dropoff is)
The second real alternative is replacing the first bus leg with a ferry leg by going to Larkspur Landing. There is the SMART train that goes there, but for some wild reason drops people off a 15 minute walk from the ferry and then has no timed transfer.
I did the journey dozens of times and never completed it in less than 2h 30m but more commonly was 4h and had more than 1 occasion where it took much longer than that.
Edit: Also Google Maps says San Rafael to Palo Alto will take 2 hours give or take a few minutes on public transit, with 3 buses, but the middle one you could easily cut out with a bike or a 4 block walk. That doesn't really seem absurd at all for an occasional trip. People do 2 hour drives for an occasional trip and no one bats an eye.