Biking along the Mosel

for whats its worth, we drove the stretch from cochem to bernkastel-kues and there were plenty of nice towns, nice scenery etc. also plenty of people riding along the river. which is what we would have done if we had more time. we enjoyed the area much more than the rhine.
have you checked google maps to see how far you are considering? given you have only one day?

Take the train to Bullay - nice quiet place to stay and a good place to head out by bike. Much of the riverside bike path is separate from the road.

Bullay, on the right.

Scene just outside of Bullay

Near Bullay the river does a big loop and almost runs into itself.

Nice place to stay in Bullay (there are several other options as well, including the bike-renting innkeeper below.)

One of the Bullay innkeepers rents bikes:
https://www.romantic-germany.info/infrastructure/infrastruktur/Fahrradverleih-Werner-Budinger_Bullay/deskline-details.html

A ferry connects Bullay to Alf on the opposite river bank. The ferry operator rents bikes too:
https://upload.wikimedia.org/wikipedia/commons/d/dd/3_6_Bullay_%28Hintergrind%29_F%C3%A4hre_nach_Alf.JPG

From Bullay you are a very short train ride from Cochem (greater variety of restaurants and activities than in Bullay.)

Here is a detailed bike map of the Mosel River trail. Shows distances and elevation changes in the lower chart. about 30 km from Bullay to Cochem. Also there are other routes you can take. The Regio Radler bus runs a regular schedule along the river. It has a bike trailer. You do need to reserve a spot. And you can take bikes on the trains outside of rush hour.
https://www.tourenplaner-rheinland-pfalz.de/en/tour/long-distance-cycle-trail/moselle-cycle-trail/3371404/#dm=1
https://regioradler.de/pages/en_en/start.php?lang=EN

Edit - You can either buy a Rheinland-Pfalz Ticket for 29 EUR for 2, and have free use of all regional transport in the Land, or a VRT TagesTicket Gruppe Netz (all-zones) for 25.40 EUR. Then Bullay is as far down river as you can go.

Or - take the train to Cochem, rent bikes there and bike to Beilstein and back. There is a bike path on both sides of the river most of the way.

Great helpful info! Thanks for your tips!