It is all ok to have bounties which do grant progress in strikes but stop tying them exclusively to them. Rather create them like "do it in patrol or do them faster in strikes". Basically we should able to do them EVERYWHERE, but in strikes we get bonus progress. I would rather play patrol for the vanguard bounties than sweating my ass of in strikes to get the kills before my teammates do.
Load up a nightfall and go into a lost sector. Thats what I do to avoid fighting other people for kills :)
Like the other guy said just load up a Nightfall. Just running around the patrol area should be fine, the good thing about that is you can use the modifiers to make it easier. Grenades, heavy ammo etc.