We have bassets, and they are sweethearts of dogs. They are the most laid-back dogs I've ever had. They are very low-energy. Sometimes we joke that they are cats in dog bodies because they nap so much. Labs, in general, are more energetic, so that could make a difference in personality. I will say that bassets do have a tendency to wander if they are not in a confined area. They tend to follow their noses.

Here is a link to a basset forum, and there were (and probably still are--I just don't frequent that site much anymore) several "bassador" owners there who may be able to give you some good ideas:

http://www.basset.net/cgi-bin/ultimatebb.cgi

Hope this helps!