ÜF = price of overnight stay per person with breakfast
VP and HP = p/p price for full board and half board options
You pay per person, in other words, for a typical family room with 4 beds and a bath - not by the room - and price varies by meal arrangement.
I have no idea what David means by a "hostel" or "B&B" town - but IMO the problem with Bacharach's hostel is its location, which is high on the cliffside above town. Train travelers will need a taxi or sturdy legs for the 500 uphill stair steps from town. This of course discourages coming and going. If you are driving it might work for you but before booking you should still have a look at where the parking area is - I don't remember that info.
Bacharach's other room options must be carefully vetted. Some are WAY too close to the train tracks. You will find quieter places (like Im Malerwinkel) along Bluecherstrasse, which zags away from the river on the north end of town. Check the reviews carefully for noise complaints wherever you book.
Rick Steves advises staying in Bacharach. But there are several good towns you can stay in. A hostel that's right in town near everything is the Kaub hostel, in a most attractive historic building (if you really want a hostel.) But it too is institutional and can be very crowded. Why not just get a vacation apartment? I've stayed solo, with my wife, with my wife and daughter, and as a multi-generational family of 5 in Bacharach, Oberwesel, St. Goar, Osterspai, Koblenz, and Boppard - in hostels, hotels, private B&B's, and apartments. The Bacharach hostel was OK but also overcrowded - seems like its 170 beds are always full. Our favorite stay was the inexpensive 2-BR St. Goar apt. "Rhine View" overlooking the river. Great owner, apartment fully equipped, steps from everything. All the other towns have apartments too, including Bacharach. I see Rick's insistence on Bacharach as the top place to stay as extremely arbitrary. There are good reasons for staying in these other towns - including the fact that they tend to offer more to see and do - instead of Bacharach, but I wouldn't recommend one without knowing more about what your plans for the area are.