They can indeed bid back to the RHS of a long haul fleet at a later date. This is what a lot of people used to do until the NAPS command taxation made it a really financially foolish thing to do. One of the reasons short haul commands have gone so junior is that NAPS members are unwilling to sit in short haul as a Captain for an unknown period of time (waiting for a long haul command), and they no longer have the option of going right to left more than once due to the taxation penalty being applied twice if you do.
For those asking about command pay scales, FO payscales are 75% of Captain's pay at all paypoints and on all fleets. It is very simple.