Most the bottles i have seen are dishwasher safe, top rack only, although i have washed some on the bottom without any obvious side effects, you may turn the heated dry off if your dishwasher has it though as they may warp.
Many hydration products such as bottles and bladders are made of TPU (Thermoplastic Polyurethane) or some variation of it. One thing you might try is adding the juice of a lemon, filling it with water and sticking it in the freezer.
Leave enough air/room so that it doesn't expand and burst.
Once frozen, remove from the freezer and let thaw. For TPU hydration bladders this process works wonders. I would assume it could also help with bottles as well but have not personally tried it on a bottle.
One other idea is a product from a company called Bottle Bright, which make a food safe, chlorine free tablet that is used to clean heavily used bottles. Their website can be seen here: Bottle Bright They are just a drop in tablet, and are safe for any kind of container.