Julie, Berners are suppose to be a dry-mouthed dog. It's up to the breeders to chose correct breeding partners for their dogs to keep this good feature in our future puppies.
A wet mouth comes from loose flews. The lower lips on the sides. If they are loose/hanging then air gets in the mouth and stimulates the saliva glands. This is a different situation from a dog that is anxious to have a treat and the saliva flows in anticipation of food. So in looking at puppies, first look at the parents for a tight lipline and then look at the puppies for the same. It will not be so obvious in a puppy but look for a saging of the lips at the sides/near the corner of the mouth. In almost 29 yrs I've only owned one dog with a wet mouth and there were never strings of saliva but just a wetness to the sides of the mouth which he loved to rub off on my clothes. As much as I love the dog, I hate a wet mouth. Sandie Hawkins Sajan (Berners/BMDCA member since 1975)