Can a Bayern ticket be used for train from Wurtzburg to Rothenburg?
Can ticket be used any day that week or specifically on the date specified?
1.) Yes.
2.) The Bayern ticket is good only for the date printed on the ticket, and only on local and regional trains (no IC, ICE, EC, RJ trains.) On weekdays it is good only after 9 am, Saturdays or Sundays at any hour.
The Bayern-Tickets are unlimited at that price (the never sell out), so there is no advantage to buying them ahead. Purchase them just before travel, for that day.
The train from Steinach (on the main line from Würzburg) to Rothenburg is a regional train. Except for an IC leaving Würzburg at 11:27, the only trains from Würzburg that stop in Steinach are regional trains.
Here's DB's Bayern map, which I believe you can only access from the German part of the web site.
You may know this but a regional train is the same as saying local train. They are the smaller, slower trains that stop at every station along the way. When you visit a smaller town, like Rothenburg, you need to use a regional train because others won't stop. Remember it's listed on schedules as Rothenburg ob der Tauber (or odt).
Regional train are designated as RB (Regional Bahn, stop at every station), RE (Regional Express, stop at major stations), or IRE (Interregio express). The Bayern-Ticket also includes all forms of conveyance (S-/U-Bahn, streetcars, and buses) in metro districts, like MVV (Munich), VGN (Nürnberg), and RVV (Regensburg).