I just bought and pre-ban AR with a 20" barrel and I am interested in putting a new Bushmaster M4 upper on it.  What is the shortest length barrel I can legally have?  I would like 14.5", lf legal.  Thanks

If you didn't want to go through the trouble of registering your rifle as a SBR (short barreled rifle) then the shortest legal length is 16". You could get the 14.5" barrel but you would have to permanently attach either a flash suppressor, muzzle brake, or barrel extension of some kind to make the barrel length the 16" minimum.
If you wanted to go through the trouble of registering the rifle and paying the tax then you could have any length you want. That's supposing that SBR's are legal to own in your state.
Most people will tell you its not really worth the hassle.