I just cut them into small pieces and put them in the lawn bags. I've never had trouble with them.

Actually, for me, the lawn and leaf bag is a good option. I cut them up to smaller pieces to fit in and the slightly thick bag contains them without any problems.

Another way I have done here in my city is that I just bundle them up and put them where they will be picked up by the city. In our city, we don't actually have to call and schedule a pick-up of large garden refuse like tree branches. Just set it out and they get it.

By the way, in case you have ever wanted more of that rose for you or friends and families, growing the cuttings into new bushes is a good way.

Burn them! We put our dried rose branches in the fire-pit and roast some hot dogs. It is a lot easier than bundling or bagging.