The new airport bus will be run by STM.
It will be seven bucks one way, which includes a 24 hour pass on the Metro. If you already have a CAM or TRAM monthly pass, you're covered.
The bus will stop at 7 locations downtown, including Berri-UQAM and Lionel Groulx. The rest are hotels along Rene Levesque.
The bus route is 747 = 7 stops for $7.