Isn't there a day ticket similar to the Bayern ticket but for Northern Bavaria and at a lower price?
No. Well, if you are traveling entirely within the Verkehrsverbund Großraum Nürnberg (VGN), which covers a large part of northern Bavaria, there are day tickets for less than the Bayern-Ticket. For example, for 16,80€ for 6 people (max 2 adults) you can get a TagesTicket Plus (Verbundweit) for a round trip from Nürnberg to Rothenburg. There is also a Bayern Regio Ticket (for all of Bavaria, not just the northern part) for round trips of less than 100 km in Bavaria, but these are not day tickets.
Yes, the VGN Tages Ticket Plus will take you as far from Nuremberg as Bayreuth, Bamberg and Dinkelsbuhl.
Would that ticket get me back to Nuremberg? Or would it only be good for one way?
It will get you back. It's good for an unlimited number of trips on one day within the VGN travel zone. If you buy it on Saturday, however, Sunday is a bonus day - use the same ticket again for Sunday.