Does anyone know the availability and approximate prices of Zimmerfrei (B&B) near the train station in Bremen and Lubeck?
First, Zimmerfrei does NOT mean B&B. A B&B is a "Privatzimmer". Any reputable place in Germany has breakfast with the room, so a room in a Gasthaus or Pension could also be considered a B&B.
Zimmerfrei means the same as vacancy. It means that they have a room, and it is available. Zimmer belegt means "room occupied".
Your best source of information on accommodations (Unterkünfte) is probably the town's own website, www.bremen.de or www.luebeck.de. In my experience, Privatzimmer in larger towns are usually well outside town, not near the train station. That's why I go to small towns, where the B&B type accommodations are nearer the train station.
BTW, in my experience, Privatezimmer are often, but not always, run by older people, pensioners maybe, whose children are gone, and they have a few free rooms to rent. These people often don't speak any English. With your lack of knowledge of German, how are you going to communicate? You should be looking for *** hotels, where someone on staff has to speak English.
I have had the best luck searching for rooms in towns/cities at Hotel Reservation Service.
Once you pull up the hotels for the town, click on the rail road button and the site will sort the choices on the distance from the rail station. Even if you decide to google and contact the hotel directly, you will know the price, the hotel location and that it had vacancies on the dates for which you queried.
I usually also make reservations through HRS as they have competitive prices and you get a message back with the terms clearly laid out. I have read that HRS is the largest hotel reservation service in Germany. They are better in towns than small villages.