After a cleaning and draining as much as possible, I put mine - upright and uncapped - on the back seat of my car while it's parked outside, windows up, at work. 1 - 2 days of this is usually all that's needed to get them completely dry.
But YMMV, I live in California and can count on sunshine (and therefore a hot car interior) for much of the year.
The hoses take longer, often 4 or 5 days. I remove the mouth piece and drape them over the back of a front seat with one of the openings as near the top of the seat as possible (think upside-down "J").