If you have two tanks, or a splitter on your line, you can purge the bottles in a similar fashion to how you are filling them.
I use a pneumatic air gun (is that redundant?) with a hose on the end to get the CO2 to the bottom of the bottle. Purge, fill, cap.
It's helpful to have an assistant, if you can work that out.
EDIT: I would also recommend turning up the CO2 pressure on the keg for a day or so. Overcarbed when you are bottling is OK since you will lose some CO2 in the process.