Yes, but my answer to "where do you want to go" is so very simple: "Anywhere I can go!" It boggles my mind that in order to get answers, I have to name all the places I'd like to go. And if they are all places I can't go, I would think, after I've named a dozen such places, the agent would try to help. But that is really asking too much!
As you say, some trains may have a baggage car.... The trick is to know which train, right? So I thought I'd ask. But that information appears to be kept on a need to know basis, and I, evidently, don't.
How would the person you talked with know the answer to your question?
The person you talked with would have to sit there and look up each and every place on the website, just like you can do, in order to give you the answer to your question. And that would take him/her a very long time and tie up the phone needlessly.
So just start looking up each place in the general area where you want to go, and see if you'll be able to take a bicycle there or not. It's that simple.
BTW - you can load and unload a bicycle in Sacramento.