If we wanted to get there faster, then I don't believe our ticket is
for the entire day, is it?
Day passes like the Bayern Ticket are not valid for long-distance, high-speed trains (like the IC, ICE and EC trains) which would shorten the travel time between Munich and Nuremberg.
These faster trains require the purchase of tickets (tickets that get you to Nuremberg, but not all around Nuremberg at will on public transport.) Saver fares bought in advance might be a good option if you can keep a schedule. Got kids? Kids travel free with parents on these. See the details. Then get the VGN pass(es) for getting around Nuremberg (if you need them.)
The Bayern ticket will get you to Nuremberg (and back) on the more time-consuming regional trains on weekdays only after 9 am. So it's better to use this day pass on a Saturday or Sunday, when there is no restriction on leaving earlier, and you can squeeze more time into your day. (And no, you won't need the VGN ticket if you have the Bayern ticket.)