The train journey from Jasper to Vancouver is great and if you have the option I would definitely include it as part of your adventure! Via Rail is also very good to deal with when it comes to bikes and tickets can be flexible. They also provide the box and will help you pack it up. Greyhound on the other hand sucks, I would not trust them with my bike and every time I inquired about using their service to transport a bike they were neither receptive nor co-operative.
So to sum up:
Via Rail – I always had a positive experience and I’ve traveled on Via many times coast to coast.
Greyhound – I have always had a negative experience and I used their service all over North America.
Gordon p