Cruising to Koblenz is possible but generally less desirable than a shorter cruise. The scenery goes downhill as you approach Koblenz, and it's better to stick with the most spectacular part of the river.
And that best part of the river is from Bingen to St. Goar (or to Boppard, further north.)
Map of the core scenic area, where the demand for cruises is strongest:
https://gruppentouristik.com/sites/default/files/anbieter%202/Bingen-Rüdesheimer%20Fähr-%20und%20Schiffahrtsgesellschaft/Rheinlauf.jpg
So if you just jump on a boat in Bacharach you are guaranteed to miss half the best scenery.
From there you will need to catch a train south to Bingen Rhein stadt station, walk to the boat docks, and cruise north to either St. Goar (Rheinfels Castle ) or Boppard, then catch a second train back to Bacharach.
It's a little easier if you stay in St. Goar, Boppard or Bingen - then you have just one train ride. The town with the finest river scenery, and hotels that allow you to enjoy the view, is St. Goar. Here's a view from the St. Goar side across the river. If you stay there, you can of course still pay a visit to Bacharach if you like by stepping off the train on the way to Bingen, or off the boat on the way back to St. Goar. St, Goar is also convenient since Rheinfels Castle is right there (tour it any time you like.)
Bacharach's hotels are unfortunately all set well back from the waterfront behind the railway.
One good sightseeing option after the cruise is to take a tour of intact Marksburg Castle - the best Rhine castle of all. To do that you cruise to St. Goarshausen instead of St. Goar (just opposite each other on the river) and then take the 20-minute train ride to Braubach.
Map with railways showing the train route to Braubach:
http://www.loreley-info.com/eng/rhein-rhine/walking-hiking.php
In high season, KD cruises from Bingen leave at 9:30, 10:30, 11:30, 14:30 and 16:30 - about 1.5 hours to St. Goar or St. Goarshausen, abouit 2.3 hrs to Boppard.
Bingen-Ruedesheimer cruises at 11:15 and 1:15 fill in the lunch hour gap in the KD schedule:
https://www.bingen-ruedesheimer.de/pub/media/wysiwyg/Fahrplan_2020/Fahrplan_DE/Loreleyfahrt_Fahrplan.pdf
It is possible to do your cruise ON THE WAY to your hotel from FRA airport that first day...
Train to Bingen Rhein Stadt station, walk a few minutes with bags to dock, board with bags and cruise to St. Goar - then check in at a hotel there. Or if you can't get out of your Bacharach reservation, catch the train in St. Goar back south to Bacharach (10 min. ride, hourly service.)
