1) Contact a household moving company such as Allied Van Lines, etc. (read today that Allied Van Lines shipped 8,800 motorcycles in North America last year), and;
2) Try to find a charter air carrier that flies from LA to an airport near where your motorcycle is. Then call them and ask what they would charge to bring the motorcycle back on a standby (space available, not time critical) basis. The price might be surprisingly low - it only cost me US$ 900 to ship a 350 kg Honda ST1100 from Canada to France this summer, by air.
If the airline you find flying that route has widebody aircraft (e.g. B-767, DC-10, A-330), then the bike could just be strapped on a simple wooden pallet and shipped like that. You'll need to have less than a gallon of gas in it, and the battery disconnected. If they only fly large narrowbody aircraft (e.g. large single aisle aircraft, e.g. A-320, B-757) you might have to take the front wheel off, to get the overall height low enough that the bike fits into the plane. If they only fly smaller narrowbodies that are not designed to handle palletized cargo (e.g. DC-9, B-727) you might be out of luck.
Used motorcycles are classified as 'dangerous goods' for air freight, but there is a very straightforward set of instructions for both you and the airline to follow that explain how to pack it. It is packing instruction 900 from the IATA DGR (Dangerous Goods Regulations) book.