Bamberg is a city in Germany located in Upper Franconia on the river Regnitz close to its confluence with the river Main. Its historic city center is a listed UNESCO world heritage site. Bamberg is bordered by the A70 and A73 in the north and east and is just about 30km far away from the A3 in the South.
For going towards Frankfurt or Munich, you can choose to start at the A3 instead of using the A70 or A73. For both directions you can go by bus to the service station Steigerwald. From the main train station in Bamberg take bus #978 to Mühlhausen and from there bus #207 to Weingartsgreuth, which takes at least one hour. Weingartsgreuth is only about 700m far away from the service station. From Mühlhausen it is about 4km to Weingartsgreuth and 2km to the next on-ramp. You could also try the following but it is less likely to find someone going to A3. Most traffic will be going south.
South towards Nuremberg
From the Main Station Entrance go to the left and walk over the tracks (left again), follow the road (Starkenfeldstraße) till you reach a main road (Berliner Ring), A73 is straight on. If you prefer asking there is a Bavaria Petrol station about 1km to the right along B22, which will lead to A73 and B505 (dir. A3). A lot of locals stop at this station so it is a great spot, got a ride there plenty of times but note that most traffic will be going south and it might take some tome to get all the way to A3.