First, the BBB is great, but they are a paid service, so not everyone will be listed with them, only the ones who want that endorsement. This should not put you off from a small-time contractor who probably will do a fine job.
However, I do recommend everyone calling and speaking to their satisfied customers, so ask for some of their happy clients.
If they say yes and give you some names and numbers, then actually call these people and ask.
If they don't and make some excuse like privacy, etc. don't buy it! Here is why: they will not be giving out any information that is not already public in some way, so privacy is not the real reason, and if someone did a good job for others, you would think that they would be begging you to call them!