Speaking as the owner of a Cavalier who in his younger days would happily run around off-lead for 10 or 12 miles, most Cavaliers would be happy with plenty of exercise - with several provisos.
1. Cavaliers on long walks don't seem to tear around like collies and whippets - my Oliver trots steadily (except when sighting a pheasant or rabbit!), enjoying sniffing the ground and investigating the undergrowth as he goes, and can carry on like that for many miles - so running beside a bike would probably not suit them. (Put yours in the bike basket!) It's a matter of physical differences dictated by original function - bursts of speed herding sheep or chasing hares (collie or hound), or steady progress in thick undergrowth hunting for game (spaniel).
2. Start exercise gently if you have a young one - 5 minutes for every month of age is a good rule of thumb.
3. However carefully you choose your Cavalier from the health point of view, many of them will have a heart murmur by the age of 5, so concentrated exercise like running beside a bicycle could be damaging, although it becomes even more important to keep them slim and fit. If your Cavalier does have a murmur, you will need to cut down drastically on exercise in hot weather.
Having said all this, I think my greatest pleasure as a Cavalier owner is walking in the country with my dogs, watching them enjoying themselves. And in my experience, one of the great pluses of Cavaliers is that they love a long country walk, but they don't wreck your house with boredom if they don't get long walks for a few days!
I think if I had your lifestyle, I might look at one of the bigger spaniel breeds, like an English Springer, rather than a Cavalier (it's the bicycle bit that concerns me, rather than lots of walking).
Hope that helps,
Kate, Oliver (who still enjoys 5 miles in spite of SM), and Aled