How damp are we talking here? Unless you're camping in a swamp or something, seems like most decent bags handle a little moisture just fine. My old bag gets a bit clammy sometimes but never ruined a trip. Guess it depends what kind of camping you do.
A backpacking guide once told me to put a hot water bottle in the foot of the bag before bed. It drives out the damp air trapped inside and pre-warms the sleeping space. Makes a huge difference when the temperature drops overnight.