I'm not sure what, but you've got to be overthinking something here. Check valve is soon after the reg, w/ say 3' of tubing then going to the counter. Pull apart check valve and fill line w/ water, reconnect. Don't touch counter. At all.
I've just been doing that way because I haven't really had anything to fill the line with up until a few months ago. (Creature of habit I guess...) I guess the simplest way to do it would be to just unhook the check valve under the bubble counter and just fill it right there like brohawk suggests. (with a syringe or something)