There are definitely shops to rent bikes in Canmore, but you are going to end up on something like a Rocky Mountain Instinct, or another trail bike. We really don't have any major DH/shuttle stuff here. It's all pedal access. The locals who race are usually on something like the Blur TR because of the rougher nature of our trails. The main two places to rent decent mountain bikes are:
Transports up at the Canmore Nordic Centre:
Trail Sports Inc.
Rebound Cycles-which in is the downtown:
Canmore Bike Shops | Bike Repair in Canmore
One of the great things about Canmore is that you don't need a car, there is a lot of riding right in town. Check out Trailforks, it's a great place to start for trails, but the classics are:
Canmore Nordic Centre-a typical loop is up EKG East to EKG, enjoy the views in the mine meadow, climb Odyssey, descend Odyssey, climb back up Road to Ruin into EKG back to the parking lot. There are lots of other trails here, the Nordic Centre has been the site of many races including a few World Cups in the late 90s, Canada Cup and National Champs, as well as hosting an annual Enduro.
The CAMBA beer loop on the north side of the valley is also a good intro to that side, and there are some fun sections to explore off that loop (Upper Slabs in Horseshoe)
Pedal for Pints, presented by CAMBA
p4p.camba.ca
The Highline trail is also a must do for a XC/all mountain rider. Great flow, challenging climbs.
You can take the Roam bus to Banff and ride Stoney Squaw/Tunnel Trails
A classic XC loop in Canmore is Canmore Nordic Centre Banff Trail/singletrack to Rundle Riverside to Banff and then back on Goat Creek fire road, where you arrive at the top of the Canmore Hill where you can descend Reclaimer (Canmore black trail)
If you are motivated and have the time, you can climb up Canmore Hill and do a section of the High Rockies-there may be a shuttle service to drop you off up there, but it is XC riding through amazing mountain terrain.
Carrying bear spray and making noise while you ride in Canmore is recommended, we do have lots of wildlife around here. Negative encounter are rare but it's good to be aware and prepared.
Hopefully that is a bit of a primer for Canmore to get you started.
Cheers