All pests of this sort begin with eggs laid by a winged adult on the foliage or stems during the present season.

Insecticides should not be regarded as preventative. You should apply them only when pests are present and doing damage. In this case, with only one rose affected, I would simply pick them off and squish them. They will probably not return this season after you wipe out this generation. You can prevent serious damage if you scout for them every day for a while.

They are either sawfly larvae or moth larvae, probably sawfly from the behavior you describe. Either can be killed with the relatively safe insecticide spinosad, sold under a variety of labels that will turn up in a web search. You may need to get it by mail. However, any insecticide will harm beneficial insects as well as pests.

Thanks for your careful observation and description, as opposed to the "Help!!! Something's eating my roses!!!" posts we sometimes get.

I usually just squish them. They don't usually get out of hand here. Maybe a beneficial something eats them? And I have a bunch of birds.

They have gotten out of hand, though, so I very, very rarely use some spinosad and pick any open blooms off first, so the bees won't get close to the bush (hopefully). I certainly don't use it unless my buds are getting eaten very badly (which may be a different kind of caterpillar in any case; I see lots of things on my roses, lol). The spinosad works, but please consider the bees if you choose to spray your buds.