I hand wash my cycling clothes every four days or so – usually with powdered detergent. But I’ve recently been using a laundry soap bar that you can scrub into the fabric and better remove stains.
I make sure to go to a laundromat every 3-4 weeks at a minimum. This gives my clothes a much better wash than I can do in a basin and keeps them looking pretty decent.
If you don’t feel like cleaning your clothes regularly, you could always just carry a few more clothes than necessary. After all, clothes don’t weigh that much and pack quite small. Then you can just go from washing machine to washing machine – food for thought.