The plant you bought is undoubtedly a grafted plant ... the named variety of rose grafted to the roots of another. It sounds as if the rootstock has produced suckers. These suckers compete with the named variety. Carefully dig beside the sucker until you can see where it emerges from the plant. If it is below the bud union (the knotty part where the named variety of rose grows from), carefully tear the suckers off. Don't cut them, because that leaves parts behind that will just grow right back and start the problem all over again.