Since you do not say where you are ultimately flying to and on what carrier, I can only give some advice based on past experience.
If you have to ship the bike internationally, check the prices to ship it versus on the plane. It can be expensive either way. If flying on United, as of two years ago, you could take the bike on the plane unboxed but some of the other stuff had to be done, i.e. turn handlebars, remove/reverse pedals, etc. I heavily padded my bike with bubble wrap and it arrived fine (going from US to Edmonton and also Calgary another time).
If home is in Canada, consider the train and/or bus if you have the time. You can easily observe the handling of it. I have traveled by bus several times in the US without an incident but every time I did have to box it.
As I live in the US and if had a lot of spare time, I would consider taking the train from Jasper to either Vancouver or Toronto and then take the train/bus from there to home depending on which was easier. Most Amtrak trains now allow your bike to be rolled on (with bags attached) so it is quite easy. Costs up to $20 but worth it to me.
I have had the worst luck with SWA but then they pay for the damages promptly but after a lot of paperwork. I always takes lots of pictures before I box it, before it is placed in the boxed when padded, and the undamaged bike box when checking it in. Still it is a pain so I tend to either drive a one-way rental car or bus/train it when possible instead of flying. It may cost a little more but for me it is worth the easy way of doing it.
After you get home, come back and post about what you did and how it worked out. Hope you have a great trip!
