It's worth remembering with Amtrak that "no checked baggage" is not the same as with airlines. It just means you can't check bags into the baggage car. You can "carry on" two bags up to 23 kg each, and I've never seen anyone weigh a bag on a train! (I suppose they might if it "looks" huge.) For that matter I've never seen anyone enforce the two bag limit on a train, but the bus part of the trip may affect that in this case.
SF to Yosemite for US$38 it seems like a pretty good deal (assuming you can't find a car ride with someone, and that you're happy to buy a non-flexible ticket).