My first thought is that if you keg, and might want bottles, you might as well get a counter-pressure filler, or a beer gun. It's nothing compared to the expense of the keg setup, and I've enjoyed my counter-pressure filler so far. Bottles are a very cheap way to store beer after you've force carbed.
As for the immediate problem, do you have any emtpy growlers lying around? I don't use my counter-pressure filler when filling a growler (search "exploding growlers"), because I'm worried about it blowing up on me. They seem to last a good weekend without becoming noticably flat.
If you don't then I would try the morning for sure. I've never tried filling a bottle without a CPF, but the air-to-beer ratio will be a lot higher in a bottle, so I'd be nervous too. I'm sure someone here has tried it, and will chime in soon.