Loose BB
 

I recently bought a new bike and I have about 300 miles on it and the Bottom Bracket has gotten loose. So loose that I can spin the splined nut with my fingers. I don't have the tools to tighten it back so what do you think my LBS would charge me to tighten it? Also, is this very common?

If you bought it from the LBS, there should be absolutely no charge and they should apologize for having it come loose. If you bought it mail order or from a private party, I expect the LBS will want at least $10 as they will have to remove the crank to get to the bb cup. For about the same $10 you could buy the needed tool.

Not common at all, if the bottom bracket was installed properly. In my 20+ years of riding, I never had one come loose.

+1. Torqued properly they should never come loose by themselves.