I wouldn't recommend cycling on the Barlow. Period. The traffic volume alone isn't worth the risk, nor the virtually non-existent shoulders. Get a cycling map from the City of Calgary and stick to the pathways.
Here's a link to an interactive map I found on the City's website:
http://cocnmp.com/bike_and_pathway_m...thway_map.html
I also recommend going on 1A (Bow Valley Trail), not HWY 1. Again, the sheer volume of traffic is why. Once you reach Canmore you will be forced onto the freeway From Harvie Heights in Canmore, to Banff Ave. in Banff.