What to do when your rose bolts?
Roses for most part are budded; except for ground cover, shrub, landscape or miniature roses classes. A budded rose has both root stock and the desired variety. What can happen in hard winters is the desired variety gets damaged to the point of being stunted or killed out. Then the root stock takes over and will send canes up outside the bud union to acquire the light it needs to process sugars. This is known as a bolting, when this happens to my roses I follow this thought process.
First if the only thing alive is the bolted canes (canes growing from below the graft), I yank the plant. If the desired part still has at least 3 good canes left then I count how many canes are emerging from below the graft. If there are more than 5, I take the plant out. If there are less than 5 canes I cut them to the ground and see how it goes. I watch how the plant grows over the coarse of a couple months to a growing season. If the plant refocuses it's energy back into the desired variety, great we can keep the rose. However if the plant keeps sending up canes from below the bud union and the desired part remains stunted then it's probably time to yank it, for it is probably not going to recover.