Are you set on using bib shorts? I prefer using just shorts so they take up less space when packed and are quicker to dry when wet.

I go pretty minimal with riding clothes: two pairs of padded lycra shorts, two lightweight synthetic tops and two pairs of short Smartwool socks.

I camp, rather than stay in hotels, but I usually end up somewhere with at least cold running water. I carry a small collapsable basin and a bottle of Campsuds.

As soon as I reach camp each day I take a bird bath (unless there's a shower, of course!), change into my camp clothes, and wash the day's laundry. After washing, I hang the day's clothes to dry. Often they're not quite dry the next morning, so I'll strap them to the sides of my panniers and wear the other set.

It's a quick and easy routine. Personally, I prefer to take this little bit of time each day than to carry around extra clothes, especially when they're dirty. (Actually, I carry a third pair of very old padded shorts as an emergency backup in case, for example, multiple days of wet weather disrupt my system.)

Every week to ten days I'll stop by a laundromat for a more thorough washing and drying.

This system works quite well for me, but like with most things in touring, don't worry about it too much -- you'll quickly figure out a system that works best for you.

Note: sorry for redundancy with SparkyGA's post -- I got sidetracked after starting mine, and I didn't see his before finishing.