You may need to edit, as I don't think what she tried would work. In their current situation, the fire is going to burn one side of the bridge, but that is going to take a few minutes. On the other side, the bandits are going to cut the other. I don't think she would be able to get over there in time.

Edit: I also had an idea of how to stop them from cutting the rope in the first place, but I am awaiting a response from Lucius.