Haven't gone that large but collectively i must have made over $1000 of stranger buys from facebook - thankfully all has been positive.
Nothing foolproof but i check their profiles (fb shows old their profile is, how many friend's they have), how many poducts they have for sale or sold + what kind, some bike sellers would have other bike related products also for sale, asking relevant questions regarding the bike (also questions only a biker would feel relevant to answer) and the product description they write helps, ask for more specifics of pictures (close-up of drivetrain etc) . Some people also have marketplace reviews if you're lucky. Also if youre lucky and they have the original invoice :)
Good luck!