They're definitely not beneficial.

They're cottony cushion scale. The white stuff encloses their *many* eggs.

Get rid of them. Then figure out why the rose is stressed and correct that.

Those would be Cottony Cushion Scale and while the usual means of control is to spray with a superior oil spray. although it may be just as easy to cut off the affected stem(s) and compost them. As Jean suggested check to be sure the soil the rose is growing in is a good, healthy soil that can aid in keeping things like this under control

And for your future reference....as a general rule of thumb, if you observe hoards of critters on a single plant, it's not likely that they will ever be beneficial. ;-)

Thank you all!! They are only on 1 of my rose bushes and not the others - yet! I hand picked them the best I could but I noticed the under sides of the leaves have lots of small bugs I thought were aphids, but might be the young cottony cushion scale. I have lots of lizards, frogs & toads which, along with the birds & bats, help keep our bugs under control. None seem to munching on the scale. Is there anything I can apply to the rose bush that won't harm the other critters? I read that even soapy water will irritate the heck out of them. I really don't know why this bush is so stressed. It looks as happy as the others until closer inspection. I amended the soil (red clay) well with organic materials, a little lime & epsom salt prior to planting in May. Everything has almost tripled in size since then, even the sick rose bush. Maybe more lime?? This is my first experience with Georgia soil - I'm a former Jersey girl!.
Thanks again to rhizo_1, jean001 & kimmsr.

Don't add any more lime unless a soil test indicates that your soil requires it. As a matter of fact, some soil testing is warranted so that you know what's going on....at least with the pH. For what it's worth, I have red clay soil, too, and my plants (including roses) thrive in it. Georgia red clay has a reputation for being some of the finest agricultural soil in the country.

Horticultural oils are among those pesticides that have a very low effect on beneficials. They work by smothering the eggs, crawlers and even adults of the scale insects. It won't harm your reptiles, amphibians, and other good guys as long as you don't spray it ON them. ;-)

As always, read and follow the directions on any product that you choose. If you do that, you can apply most of these products safely and effectively.

Which "horticultural oil" you use (dormant or superior), if you use one, will determine whether beneficial insect woul be adversly affected. Since the dormant oils are uses when plants are dormant they usually have very little affect on benficial insects, because they are not around at that time. However if a superior oil spray is used due care is necessary since the beneficial insects are around when those are sprayed, during the growing season.
However, scale on roses are most easily controlled by pruning off the affected canes and correcting any soil problems to help reduce the possibility of the scales, or Mealy Bugs, or Aphids from returning.

Thanks again you've been very helpful. We have an Ga Ag. extension in our town and I'll have my soil analyzed this week. In the meantime, I'll keep a more watchful eye on my plants for signs of harmful invaders.

Happy gardening!