You can save a lot on the tickets from Bolzano to Munich by buying in advance.
Right now the German train company has Super Sparpreis Europa tickets for May at €19,90 per person in 2d class, which is a huge discount from the regular walk-up fare of €67-€80. These tickets are non-refundable and cannot be changed. Seat reservations are €4,50 extra per person. The train is a direct Eurocity train to Munich with no changes on the way.
You can buy from bahn.de and choose a digital ticket on your phone or get a pdf you can print at home for a paper ticket.
You can also buy the ticket on Trenitalia, for the same €19,90, but it appears they will only let you purchase as far as Innsbruck. And you cannot get a digital ticket or PDF to print; you get a confirmation code that you use to retrieve the actual tickets from a machine in an Italian train station. We did this last September on our train to and from Bolzano on those same Eurocity trains (EC 84, 85, and/or 86). But we were just traveling in Italy, between Bolzano and Verona or Bologna. Since you want to go all the way to Munich, you would be better off buying from bahn.de to get paper tickets all the way to Munich.
There are also significant savings on First Class tix if you prefer that.
If you want to use the same EC trains to get TO Bolzano from someplace in Italy (EC 83 from Verona or EC85 from Bologna) you must buy on Trenitalia and will get a confirmation code to retrieve the tickets as I explained above. You will be offered the same good discounts.