Remove the old leaves and flower buds. Remove any cane sections that are damaged including areas of black bark and shrivelling. Now that your plant is established, you probably should remove any twiggy growth, less than 3/16. Make pruning cuts just above a bud eye (located at every former leaf juncture-- a bump with a smiley mouth under it). If parts of the plant don't support strong growth in late May, the canes have invisible freeze damage and should be cut back. You might prune around 2 weeks before the average date of last frost. Ask experienced local gardeners. Remove the old leaves now because they may carry fungus disease. Sounds like it is doing fine without winter care. Don't prune in fall. Whether or not to add a 12" mulch or pile of soil is a judgement call depending on whether this variety is in danger of freezing out in your climate. At least wait until temperatures approach zero. If there is deep snow cover, that gives substantial protection.

Suckers would be root stock that has come up on a grafted rose or an own root rose that sends up a shoot from the roots at some distance from the main plant. I think Mad has it right. That's the graft sending up new canes from below ground.

imagardener2 and juneroses Thanks for the fast response. I have wondered what this bush was for several years. Now that it has started blooming it is really an attention getter. Mine is more like a bush with multiple branches but is now probably 12 foot tall and covered with blooms. I don't see that many sulfer butterflys on it but there is an Iguana living in mine. Go figure. Only in South Florida.

I can't get one until next season, but will get one if it is still unknown then. He did say the little white flowers were in clusters of 5. Thanks for the replies.