Sazburg to Milan

The Bernina Express doesn't run between Salzburg and Milan. It runs between Chur, St Moritz and Tirano. So you need to first get from Salzburg to Chur, then the Bernina Express route to Tirano, then Tirano to Milan (by train).
This is very possible, you need to look up times and prices between these places. For times go to www.bahn.de or www.sbb.ch (latter is the Swiss Railways site). For prices you need to look on the three national railway sites for the three countries.

The Bernina Express is just one limited stop train that runs on this route (Chur/St Moritz to Tirano over the Bernona Pass). There are other regular hourly trains on the same route. You see the same mountains out the window whichever train you take.

Suggestion for a place to stop overnight: St Moritz, or Chur.

You can get a discounted nonrefundable ticket from Salzburg to Chur at www.sbb.ch/en once you get inside the 90 day window before your planned departure. The actual Bernina Express train leaves in the morning from Chur that time of year, so an overnight there would be needed to get that. Mid November will have short daylight hours, so that is probably just as well. Trying to do it in one day means you could be going over the pass in the dark on one of the regular trains, which kind of defeats the purpose of the long detour.
The change in Tirano is to a different station, but it is just across the piazza from the RHB station. The train to Milan is a Regionale and you can buy that ticket at the station and there are no reservations.