You might take a look at accommodations in the towns NORTH of Bacharach, in part for the VRM, in part also for the free VRM guest ticket that comes with your room at many of the hotels/inns/apartments within the VRM (and ALL of the hotels/inns apartments in the town of Boppard.) Wherever these guest tickets are issued, every guest gets one that's good for travel along the Rhine and Mosel rivers within the entire VRM zone - and not just for one day, but for the entirety of their stay.
Bacharach is of course a lovely town that you should visit. But staying there is unnecessary since it's so close to the VRM towns and the out-of-pocket cost to get there with a supplemental ticket is pocket change. There are other good reasons for staying in Oberwesel, St Goar, or Boppard instead of Bacharach too.
VRM Guest ticket info: https://www.vrminfo.de/fileadmin/data_vrminfo/PDF/Gaesteticket/Infoflyer_Gaesteticket_englisch_2022.pdf
(Note that the Guest ticket has an expanded zone of validity outside the VRM on the other river bank... Rüdesheim can be reached without a supplemental ticket.)