"For the train, I see the 7:03 (with 5 transfers) that arrives at 14:26 on DB website for 29€ per person. Am I missing something? Am I looking at the wrong thing? If there are train tickets for €48/2 adults, I would be very grateful if you could give me more details on how to find that ticket. I will get immediately!"
The 7:03 I'm looking at right now to Bingen Rhein Hbf has 4 transfers (Freilassing, Munich, Mühldorf, and Stuttgart) and arrives in Bacharach at 14:04. Make sure you haven't entered any stopover stations. You should get the same. You can walk to the KD dock from either station within 10-20 minutes. Your train schedule is for Bingen Rhein Stadt - that adds a train and would make you LATE for the 14:30 boat.
To get the €48 price, enter TWO ADULTS traveling.
Buy thoughtfully, not hastily. You are squeezing your time like crazy. There's a chance one of your trains will be late. If so, perhaps you would need to use to reach the train to reach St. Goar for Rheinfels and do the cruise the next morning. What's your time like the next morning? Would that even be possible?
OR... There's a €48 trip the day before leaving Salzburg 17:15 and arriving Bingen Hbf 00:06. Could you do that? You'd cancel your last night in Salzburg, stay in Bingen 1 night (then in Bacharach as scheduled a 2nd night...) stay at the NH Bingen, right on the waterfront near the KD dock? It's an awesome location with a great buffet breakfast. Then you'd have a decent amount of time on the Rhine - a full day.