"Banff" and "spring" could equal "snowy".

A less expensive version of that trip would be to fly into Calgary and cycle from there. I just wouldn't recommend doing it before mid-May. For one thing, there won't be much open in the way of campgrounds etc., and it could still be quite cold and snowy. However, if you are planning to ride mid-May or later, then I'd recommend something like Calgary to Banff, Banff to Radium, Radium to Golden, Golden to Lake Louise, Lake Louise to Banff, and back to Calgary.

Otherwise, for 7-10 days, a relatively inexpensive trip would be to fly to London (Heathrow) and do a bit of cycling around England.

Or you might consider Vancouver Island ... but it does tend to be a bit rainy there in the spring.