Meißen doesn't take long to see. It's basically a nice town with a
castle on top.
If a small town is world-famous and on the cover of Rick Steves books people spend two full days there. if a small town of the same size is almost unknown people barely spend an afternoon there.
2 hours are not enough for Meissen. The old town is small, but there's not only the castle but also Saxonys biggest Gothic cathedral and of course the porcelain factory. Which sadly is a bit outside, you have to walk for ~15min to get there (see here). When you visit the old town don't use the straight route from the town square up to the castle! Instead use the steep walk between the town church and the restaurant "Vincenz Richter". At the end turn right. After a few metres you cross St. Afra and the small graveyard of St. Afra. This walk offers some nice views. At the castle complex visit both the cathedral and the castle. The highlight of the castle for me are the dungeons with graffiti from the Thirty Years War (1618-1648). And don't miss the passages, which offers great views.
Sorry, I can't help with B&Bs in Meissen.
You could conceivably fit everything in Dresden in one day
Old and New Masters, both(!) Green Vaults, Turkish Chamber and Armory, Porcelain Collection, Cabinet of Mathematical and Physical Instruments, Military Museum, Zwinger, castle, Frauenkirche, old town, Neustadt, Pfunds Molkerei, Semperoper, Great Garden, Pillnitz, Blue Wonder and Funicular Railway, Transparent Factory, steam boats.... I guess this would be a very long day....