Yes, as Link showed, what I got is called a check valve. Got a pack of 5 for about $2 on Amazon a couple of years ago. They come with each enclosed in a plastic housing designed to be fitted inline, I just broke the hard plastic away to free the valve itself.
Thanks for the suggestions on how to more successfully drill the hole. FYI I tried lighter and stronger pressure, slower and faster speeds, and I just ruined a lot of bottles. I came to the same conclusion as others that the bottle wall needs to be supported from within and tried filling it with water with the cap on and also tried freezing. Sand is an interesting idea but don’t know if it would generate different results. Tape over the drill spot also is a good idea, maybe I’ll try again. And maybe pick up a unibit. Don’t have a drill press.
After having given up a couple of years ago on trying to make this work I had just resigned myself to the need to loosen and tighten the Sawyer after squeezing the bottle to equalize pressure, ultimately not a big deal. But a friend once called my kit “a cornucopia of doodads”, so in that spirit I must try to install a check valve once again.
David, my interest in a rigid bottle would be for ease of retrieving and replacing it to/from my pack’s side pocket. I am assuming that a floppy bottle would work OK when full but as it empties it will flop over and sink down into the pocket and/or not slide back into the pocket easily, and possibly with the filter on top it would be top heavy and might even fall out of the pocket.