My friend just bought her 08 Ninja 250 last week and the closest state to LA that had one was Arkansas. She told me she used this website called uship.com She said it's much like ebay and you list what you need shipped and companies/individuals will search for stuff to ship and will give you a bid. If the bid is in your price range you accept, and then get it all set up (dates, times, payment terms, etc).
The shippers themselves have a feedback system much like ebay and there are contracts that get signed and stuff so I wouldn't worry about someone with a lot of feedback picking your bike up for you and running off with it.
Some older guy and his son are motorcycle transporters and are loading it on their flatbed trailer in Arkansas and bringing it to her in Louisiana for $250. Think its a 260 mile trip down or so. Not a bad deal.
I'm bored at work so I checked out this uship.com website a little more. I was reading some customer testimonials and one guy had his gsxr 1000 shipped from eastern OK to San Diego for $585 and said the guy showed up early and bike was delivered mint.
Might be worth your time to check this out. If someone bids under the $750 you were quoted, then you just earned yourself an extra mod.
I own a Nigerian shipping company, as I am the prince of Bigboobzadaze. I am wiling to ship for a modest fee as long as you transfer a fee to a friend in need. His daughter is in need of an urgent implant surgery. She recently lost a competition, which they rely on to feed their family. If you would like to discuss this serious matter further, please reply to this thread.:sing