Damp or wet conditions will definitely deter bumblebees – they need things to be dry. Apart from keeping the roof waterproof, I’d replace the cardboard with a layer of gravel if I were you. That should help keep the moss drier, anyway.

The cardboard would make it easier to reuse the nest, but the thing is that reusing a bumblebee nest would be risky anyway. A lot of bumblebees carry parasites and other unpleasant things. Once a bumblebee colony has used a nest, these parasites will exist in the nest, multiply and infect the next bumblebee colony to move in. If the parasites multiply enough, it’ll kill the colony. So if you’re going to reuse the nest, you should really scrub it out with soap and water first, to purge any unwanted freeloaders