I use a Lowpro trekker for my 500mm when travelling abroad as this fits pretty much all my photographic kit but that is generally with BA which has ample hand luggage allowance. However most other airlines have weight restrictions which means no Lowpro, iit's great and padded but heavy without anything in it, so I use a NorthFace Bigshot ruck sack for transport to and from many destinations where saving hand luggage weight is a must. It does mean camera not being attached to the lens most of the time but I can still get most things in the bag.
When out in the field I have it over my shoulder. Using a padded wide strap this goes over my head and is slung ready for use; I don't screw a BlackRapid or anything similar into the foot plate as this would prevent easy use on a tripod (via a Wimberley Head) or monopod with (Wimberley type release plate on a pan and tilt head).
I have stitched nylon webbing loops to where the Canon strap would attached to the lens body and the strap has a strong Snap Hook that clips onto it. An alternative is to use the strap with a fairly large Snap Hook so acts like a BlackRapid strap, i.e. the strap slides through the Snap Hook, so no need to keep taking off the shoulder to use it.
This is done primarily for handholding the lens, Canon 500mm is no light weight but when your out in the field all day when on a trip this is a quick win; especially if using a monopod.
Whilst I do use the tripod and will move short distances i wouldn't walk around all day with it attached; I've seen some 500mm big white attached to Pan and Tilt heads on tripods attached to peoples backs via a scopepack, like you see on many a scope. I wouldn't dream of that as its an accident waiting to happen.
Ultimately I think its trial and error to find what suits you best, I keep amending my approach; , as I'm getting older the lens seems to be getting heavier.