You can just fill from the tap, but purging the bottle and filling under pressure makes for a more sanitary fill, maintains the carbonation better, and allows for safer long term storage.
Here's how I stabilize cider when force carbing:
Stabilizing cider for bottling is a two-step process.
First, you gotta bring down the yeast levels. No amount of sulfite & sorbate will stop a healthy yeast colony at maximum population. Ideally, filtration to less than 1 micron will do the trick, but who has the capital to spend on one of those home-sized filter units? Personally I'd rather spend it on more juice so cold-crashing and/or time to drop clear is your friend here. Rack off the lees and you should have a pretty clean cider.
Now is the time for chems. Add 1.25g/gallon sorbate, unless the packaging says different, and 6 campden tabs, assuming they're 50ppm tabs, and your pH is relatively normal (3.5-3.6). Otherwise, you may need to add some malic acid or increase the sulfite addition as per this chart:
The goal here is to immediately get your SO2 levels slightly above above what you want in the cider. It'll bind and reduce to the levels you want after a couple of days, so don't panic if you get a strange smell or taste right off the bat. It'll go away.
Adding can be a pain, as campden doesn't like to dissolve in cool cider so I boil a cup of water and add the crushed tabs and sorbate and stir like hell. Then add directly to the keg when transferring. The nice the about the 5 gallon keg is that you can also seal it up and shake the living daylights out of it for added mixing. Be sure to purge the keg with CO2 before racking.
Now you should have a stable cider! So keg and carb as usual following this table:
I recommend 2.2-2.9 vols for cider.