Ascap I do know will give sort of an advance, but the scenario I've seen on that is if you have a song that is charting or generating a lot of synchs, they will essentially give you a low-ish interest loan. Typically the real advance is going to come as a part of signing with a publishing company.
The only reason to go LLC for this type of thing IMO is if you need to try to insulate assets from creditors. Advances are not loans, IE you cannot terminate the period of a pub contract by recouping the advance ahead of time. The flip side is if the advance never recoups, the publisher cant go after your personal property. So in that case an LLC isn't going to do much for you.
But yeah I'm with Chris, even DBA's and all that are not necessary, get a TIN so you don't have to give out your social. That's all you need.