A) Running it through a rinse cycle with vinegar will get rid of the mustiness, but we’re looking to prevent that entirely.
B) Set a timer. Until you know how long your wash cycle is, set it for an hour. They’re rarely longer than that. Hit start when you start the load, then when the timer goes off, go put the stuff in the dryer.
C) Set another timer. Because laundry has three steps: wash, dry, and PUT IT AWAY GODDAMMIT. So when the second timer goes off, go collect your stuff from the dryer and put it away.