Round trip transit to Galveston

Spending a few days in Galveston 3/6-3/9 after visiting a friend in Houston. I can’t figure out the best deal in terms of transit to and from. Staying in a central location in Galveston, so I don’t necessarily need a car there, although I am looking into rental cars

I can’t seem to figure out if you can take the Amtrak transfer bus without actually transferring from a train. Any advice ?