I've always stored all my boards, both surf and sup, in a travel bag straight out of the surf and never had a problem. The only caveat is to make sure they're kept in the shade and out of the heat.
Same as Foam and Th0m0.
Note that salt water acts as a natural disinfectant and will prevent mildew. If you rinse your gear in fresh water, you should dry it before putting it in a bag, but it is not needed otherwise.