Will you be using the month-long subscription-based pass, the Deutschland-Ticket? That could be advantageous for getting an early start and traveling inexpensively on regional trains.
Otherwise, the Day Ticket for Germany (€59/2, valid after 9 am weekdays) will get you to your cruise boat and back from St Goar/St Goarshausen.
I think you will find a lot of replacement buses and long travel times on the west bank of the Rhine that gets you to Bingen. Instead... use the EAST side railway, where no repairs are underway and the less-than-dependable replacement buses are not an issue. It's still a long trip of 3 hours. You will head to Rüdesheim to board on that side of the river.
Lv Cologne 9:51, ar R'heim 12:52 with 2 changes of train. Take a short walk around R'heim.
Catch the 14:15 KD boat from R'heim to St Goarshausen (16:00.)
If this were MY trip, I would then be looking for some food; I'd likely head to Braubach for a tour of the old town zone. Braubach is on the way back to Cologne.
Lv St Goarshausen station 16:32; ar Braubach 16:53. See 3 pages of Braubach photos here. Have a walk around town and a traditional German meal at zum Goldenen Schlüssel.
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Lv Braubach 18:53; ar Cologne 21:59 with 2 changes of train.
For comparison: The fastest morning journeys along the west bank right now for Cologne > Bingen Rhine Stadt look to be around 2.5 hours. For the dates I checked in May, One-way saver fare prices for two to ride the fast trains out of Cologne, which produce the quickest rides there, range from €75 - €140. So double that for the round trip as an estimate. And they still require changing to the slower regional trains once or twice and are under constant threat from delays, replacement buses, and the sort of chaos that occurs on a busy route when construction takes place.