I've driven from Calgary to Montana a few times, but not on to Washington. We did Calgary to Portland a few years ago. That took about 18 hours. What part of Montana are you heading for? I think Coutts is still the only 24 hour border crossing in AB.

Right now gas in Calgary is around $1.15/litre. Along 17th Ave SE in Forest Lawn is always a couple of cents cheaper than the rest of the city, and the Centex that's just off Blackfoot by Inglewood is even cheaper than that on Wednesdays, Saturdays, and Sundays. If you're going down Deerfoot anyway it's work the short detour to fill up there.