Here's how I do it...
For the main Platypus bag, get a dry cotton cloth, twist it into a kind of 'rope' and feed it through the opening into the bag. Scrunch the bag in all directions and any drips inside will soak into the cotton. The trick is to leave a bit of the cloth poking out of the opening, so that you can pull it out again.
For the hose... here's the clever bit...
Get a couple of long, clean bootlaces and tie them in a knot. Thread one end of the lace all the way through the hose, then pull it so that the knot travels the whole length of the hose, scouring it of water drops, algae and any other accumulated gunge. You'll have to experiment to find exactly the right length of bootlaces and the right size for the knot to do this effectively.