For those who just want to travel around Bamberg city and make visits to nearby villages within three calendar days, the BAMBERGcard at 14,90 € is a good option. You buy it at the tourist office and it is valid on all city bus lines (901-938) up to their last stop. This includes Merkendorf, Memmelsdorf, Bischberg and other villages.
It also includes a 2 hour walking tour of the city and free entrance to 7 museums.
For more details, visit http://en.bamberg.info/bambergcard/