I lived in Jasper about 10 years ago...
At that time, Freewheel Cycle was selling used bike boxes for a few bucks a box. They didn't throw away any of the boxes that the new bikes were shipped in, so there was a huge supply. You could walk right in and they would sell them at the service/mechanic counter. They would even pack the bike up for a small fee.
Greyhound Bus and the Via train station are actually within the same terminal. You used to be able to purchase a bike box from the Via Rail baggage counter and use it for the Greyhound. Greyhound doesn't sell any boxes, but they were available at the station when the Via desk was open for business.
At the end of the summer, I learned that VIA can run out of boxes as a lot of town residents move/travel at the end of the tourist season, so it might be likely that they may be low on supplies. I would try them last.
One other note is that the boxes that they use for the train used to be absolutely enormous. As I recall, you could turn the bars and remove the pedals and the bike would fit in with both wheels on. They will probably have enough room for your panniers and other luggage, if that is important to you. Unless the boxes that Via uses are smaller now, you'll very likely need to re-pack your bike into something smaller for the airport/airplane.