When you dry a plant whole it takes longer because the moisture from the main stalk soaks into the rest of the plant as it dries and it's like the plant has a lot less surface area, and the less surface area it has, the longer it will take to dry. Because you live in such a hot climate I would assume it would be best for you to dry her whole which means washing her whole. If you don't have big enough containers to wash her whole without damage, and you think you can still make it take a week to dry, then I guess you could wash each branch separately. Because you're washing her I would probably hang her outside on the clothesline for the first day, but make sure no direct sun gets on her for long periods of time when she's hanging.