You can keg your beer then bottle from the keg with a counterpressure filler, like the Blichmann BeerGun, for sediment-free bottles. This is exactly how most of the breweries do it, and how I bottle for competitions.
You don't even need a full kegging setup, just a single keg with a CO2 charger or small CO2 tank. For around $100 (including the BeerGun):
1) Naturally carb in the keg using priming sugar.
2) After carb/conditioning, put the keg on ice/fridge for 48+ hours to absorb the CO2 into solution, just like you would with a bottle.
3) Hook up the CO2 charger/tank to provide serving pressure for the BeerGun. The first draw will pull out all of the sediment if you gave it sufficient time to settle or used something like gelatin. Then just bottle the whole batch sediment free!