There's a train line that runs along the Mosel. You can find the times at Trier Hbf (main station) or online here (in German):
There is probably a Deutsche Bahn "Infopoint" or "Reisezentrum" at Trier Hbf where you can ask for information. If you tell them where and when you want to travel they can print you a personal travel plan.
Sometimes bike carriage is limited at certain times of the day. Reservation is usually needed only on the longer distance trains such as IC and EC. You usually need to buy an extra ticket for the bike - local regulations vary but where I live for local trains (S, RE, RB) it is called a "Zusatzticket" (extra ticket). Depending on the train type you may have to use a particular carriage. Some on-platform indicators give you some vague clue about where to stand (lettered positions) but the best bet is to find a Deutsche Bahn person to tell you. Sometimes they don't know!
Don't worry too much about all this: lots of people take bikes by train so everyone is used to it.
Viel Glück beim Radfahren!
Cycle-touring, Expeditions, Adventures, Major cycle routes NOT LeJoG (see other special board)
Trier is very interesting, the Porta Nigra (black gate) was built by the Romans and there are lots of events to do with Karl Marx who was born in 1818
Cycling? Of course, but it's far better on a Gillott