The solution in a nutshell: combine a few purchased components with a purpose-designed Delrin stopper in order to make your own bladder-free hydration system!
The hard problem to be solved: bladders collapse when water is removed and PET soda bottles do not. (Well they will eventually, but not before your ears pop!) Therefore make-up air must be added to the bottle when water is removed. The way to do this is mount a small check-valve next to the drinking hose. The difficulty is that bottle tops are small and figuring out how to fit both a drinking hose and check valve was not easy.
Step 1: Design overview
1. Allow bite valve to be used with PET bottle in bicycle bottle cage.
2. Materials must all be food-safe and easy to clean.
3. Assembly should not leak when shaken or inverted.
4. Parts should be inexpensive and readily available.
As shown in the attached drawings, the main effort involves machining a tapered stopper from a delrin rod using a lathe, then tapping 1/8-27 pipe threads in it for a hose barb fitting to attach the 1/4" tygon hose. A check-valve is attached via a short length of 1/8" tygon hose. The 1/8" hose is slipped onto a short length of 0.134" hypodermic tubing that is pounded into a 0.128" hole that is drilled through the stopper. The check-valve is secured to the 1/4" hose via a dab of silicone caulk on the side. The stopper is held securely into a water bottle using an ordinary soda bottle cap through which a hole has been cut using a 3/4" punch. A short length of 1/4" hose is used to attach the acetal quick-disconnect coupling socket with valve, and then a longer run (perhaps two feet) goes from an acetal quick-disconnect coupling plug to the bite valve. The bottle is inserted in the bottle cage and the bite valve is attached to the handlebar with a pair of nylon loop straps.
Email me (alchaiken at gmail dot com) if you would like a DXF format version of the drawings for this project.