I have two options. Stay in Salzburg for two nights and one night in Munich or bypass Salzburg and go to Munich
and then travel to Berchtesgaden instead to see the alps. Given the time constraints, should I just bypass Salzburg and travel to Berchtesgaden from Munich?
Salzburg and Berchtesgaden are close, only about an hour apart. Seems like it would be either Salzurg or Berchtesgaden first, then Munich. But you didn't say where you are coming from or going to. The direction of travel might determine when to see Munich.
Expanding on what Je said, there is a bus, called the Watzmann Express, that leave from in front of the Salzburg Hbf and takes less than an hour to go to Berchtesgaden Hbf. The one way fare is €4,90. If you get an RVO Tagesticket, for €9,50, it will cover round trip on the bus, plus any other buses you might want to take in Berchtesgaden. However, the last bus back to Salzburg leaves Berchtesgaden Hbf at about 6 PM. If you want to stay later, you should use the trains (via Freilassing) and a Bayern-Ticket Single (€21). The Bayern-Ticket will cover all the buses in Berchtesgaden, but not the Waltmann Express to and from Salzburg.