Mold of snap beans is really two distinct diseases: white mold and gray mold.
White mold of snap beans
White mold is caused by Sclerotinia sclerotiorum. White mold is a disease of most vegetable crops except onions/garlic (alliums) and corn (monocots). For example, tomatoes, winter squash, cabbage, and lettuce crops are all susceptible to this disease. (photos)
Gray mold of snap beans
Gray mold is caused by Botrytis cinerea.