That is a very helpful photo, thank you! First, get rid of the black plastic--it is heating up the soil and preventing water from penetrating. Roses have a pretty extensive root system, and need the soil around them to accept water, not just at the base of the rose.
Check the bottom stem of the rose. If there is a large "bump" at or just above the soil line, the rose is grafted and most likely a hybrid. If there is no bump, the rose is probably own-root, which is preferable if you want a long-term, strong rose. Assuming you have own-root roses, cut off all dead material now, and next season, when the rose starts to grow in the spring, prune it back heavily. By heavily I mean cut the stems down individually by 1/2 to 1/3. I know, it sounds radical, and when I do it I nearly cry, but in the long run the rose is much better off.
If those roses bloomed this spring (they are very pretty!) they are just in need of a little "tough love" and will repay you with more blooms in future.