It's easy, and common.
Turn the pressure down to about 3 PSI and bleed the pressure off of the keg (It'll still have 12PSI or whatever your serving pressure is)
Attach a length of hose to the tap that can reach the bottom of the bottle
put the bottle up, with the hose all the way to the bottom
Open the tap and fill until it's got an inch or 2 of headspace
get ready to cap - Thump the bottle on the table to make it foam
As soon as the foam hits the cap, crimp it down
This way you are capping on Co2 and the bubbles have pushed out all of the oxygen