I worked out this on the Southern Upland Way. Simple idea.
Take mouthpiece off carefully, insert tube into bottle, lift up bottle and squeeze bottle to start water flowing into the sack. Simple hydraulics. The bottle must be higher than the hydration sack for this to work.
With little practice, you can cut down the amount of air entering the hydration sack. You'll end up with some air in the hydration sack, but not enough to cause problems if you bleed the sack at the end of the day.
I've not seen anyone else talk about this or haven't read anyone else doing this, so it might be a world exclusive - but I doubt it. If I've thought of it, someone else must have.
Oh, and just carry the holed bottle lid in a pocket, and have a normal bottle lid to use when you want the bottle to hold water too. Extra weight: one plastic bottle lid with a hole in it (go figure).