Ne schöner Tag dann-now sitting in a train on the way to a package trip to Germany/Sauerland now and had a similar package-4 nights in a hotel all-in with 3 meals/day and free drinks included in a very small village on the east bank just south of KOblenz some 3 month ago. From the dining room splendid view also over the Rhein and seeing overlong freight trains passing by there on west bank every few mins and some sleek white ICE too. THat hotel also offered a free pass for the local Verbund-KOblenz area, and there was an hourly VIAS RB train doing Wiesbaden-KOblenz. But as I have and still use the Deutschland ticket-excluding use of ICE- not much use for me.
There is no town named Bingham there-there is Boppard/west bank and then Bingen going south on the bend of the river, then turns east toward Mainz. This has now also been explained above-note that the RB comes all the way from KÖln=Cologne and tends to thus be late or even later and overfull-all those also not aware D-ticket users doing it all the way. Thats by Mittelrheinbahn. The RE starts in KOblenz and is by DB-north of KO that-you must know it- National Express runs an RE with that half double-deck sets in a drab brown and free wifi and even ´german dialect´ spoken english. I was on one of their RB trains an hour ago, replacing an RE much further north.
The bahn.de site (but I always use the german major one, so there might be a little less on /en/) is a splendid source of info- but for such things IF these are all in one ´Verbund´ area-this is RMV (Rhein Mosel)- can also give more of the info you ask for-network maps-old-style tabled line timetables, some even other things-this one is rmvinfo.de (there is also vrm=Rhein Main, around FRAnkfurt), but it ends between Boppard and BIngen. However, I grasp its hard to even find out where all those ´Verbünde´ are, how they are named and how far they stretch out or perhaps a bit too much for an Interrail all over EURope