Max Stout:
Whether your 1-1/4" tube size is inner diameter or outer diameter is of interest*, and silicone tubing seems like the best choice (to avoid BPA and phthalates).
(*) Said the guy whose last rushed post confused quarts and pints, *blush!*
As regards the detail of my setup, I am guilty of an exaggeration as I had not used it for a couple of years. The valve is a 3/4" and has a short piece of 3/4" hard plastic pipe coming out of the end that goes in the mouth. The other end has a short length of 1/2" hard pipe with the flexible PVC pipe pushed over it and clamped. The flexible pipe is around 3/4" internal diameter. At its other end it is pushed over the neck/screw of the bottle and clamped. All pipe sizes mentioned are internal.
Sorry for this rather nerdy description. The thrill for me was to see how quickly I could drink the 3 pints by just opening my throat. I did on one occasion sucessfully manage two lots of 3 pints with about 30 minutes between (to allow some stomach stretching).