Actually the best way I know to clean the actual bladders is with 3-4 tbsp of baking soda and a wet clean dishrag. Just enough water to distribute the baking soda but not enough that it dissolves it all and makes it non-abrasive. Leave some air space, close the top, grab both ends and shake vigorously, then fish out the dishrag and rinse.
As far as the drink tubes, IMO it's well worth the investment to buy one of those long brushes they specifically sell for the purpose. I've done it by threading clothesline of the right diameter through the tube, but it's a PITA and the brush is a lot easier.
Mechanical methods like these will almost always get things cleaner (and more inexpensively) than chemical warfare. It's only when there's a lip or a closed space, like in those caps and bite valves, that mechanical methods haven't worked for me.
Speed comes from what you put behind you. - Judi Ketteler
I've used them to clean the terlet.
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