Montréal has quite good public infrastructure for transportation needs. There are a Métro, a dense bus system which also runs at night and good biking capabilities.
Cycling
Read about cycling in Montréal 
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Bixi Bikeshare pricing , needs credit card or subscription
Pedal Montréal Bikeshare availability map and bike lanes
Public Transport
Airport Bus 747 for 10,00 CAD
Weekly ticket Monday to Sunday for 25,75 CAD
Carnet with 10 rides for 27,00 CAD, each ride 120 minutes