How to avoid re-stinking my freshly washed laundry when I only have one laundry bag?

I have laundry bags made of cotton. They are washable but actually if you wash once a week or every other week (that's what I am doing, not sure this is an option for you), they don't get too stinky in the first place (I think that synthetic fibers and especially water-tight plastic bags tend to get stinky faster).

I haven't actually tested that, though, as I try to fold and repack my clothes in my regular bag ASAP.

Simply buy two lightweight laundry bags. One for dirty laundry and one for the clean one. They're usually made out of nylon, but I'm sure you can find cotton options as well.

This is what I do on multi-day hiking trips:

I put dirty clothes in those ubiquitous plastic grocery bags.

They're large enough to hold a couple of pairs of jeans or a large towel with some space left over. And if they develop a hole or tear, they're easily replaced.

They're ridiculously easy to get hold of in many places in the world. Just go buy food at a market somewhere, which you were probably going to do anyway. Or drop by my kitchen and I'll give you a few dozen.

This won't work in places that have banned such bags, like Rwanda or San Francisco.

With certain caveats: turn your bin bag inside-out.

Main caveat is that the outside of the bin bag must be reasonably clean. So, no good if you've carried it 5 miles through a duststorm to the laundry. Probably fine if it lives in your backpack and then you've carried it down the corridor of a hostel.

Secondary caveat: if you put wet clean laundry in it, it'll be wet, so you'll need to turn it back outside-out and dry it along with the laundry.

As far as I remember I've only used this technique when the main problem is mud rather than stink. But since the reason you're using the bin bag in the first place is that it's stink-proof this ought to work.

Not speaking from experience, but you could take a towel and wrap the clean clothes in it until you can clean or organize a new bag. That's probably what I would do.

Besides, every traveller should have a nice big towel with him/her. :)

Bring your suitcase to the laundromat, and put your clean clothes in it. Optionally, fold them first.

Everything's stinky goes in the stinky bag (a simple plastic bag). And most often the stinky bag goes always in one specific backpack folder.

Everything else, being clean, wet or not, goes directly in another backpack folder, no need for a plastic bag. I mean, it's simple: dirty things with dirty things, clean things with clean things.

I find that bringing the whole roll of bin liners would help, as they are not small, and can cater for a large number of days.

I use a series of ziplock bags, often collected into one plastic grocery bag, a bin lines or these days one of the thin foldable bags you can buy instead of plastic bags.
The very smelly things go into one ziplock, the clothes which have been used but are not really dirty in an other. The longer between laundry days, the more bags in use.
All those ziplock bags go into the bigger bag.

After emptying into the washing machine the ziplock bags are zipped closed, keeping the smell inside.
The clean clothes (dried if possible, wet if not) go into the bigger bag, which is still clean smelling.
If the clothes go in wet, the bigger bag goes on the line with the clean clothes.

But as it always rains when I put any laundry to the open air, even in a desert, I prefer dry my clothing in a machine.

For shorter travels I use the same ziplock bags system collected in a bigger bag, only to come home with me before laundry day. Ziplock bags often start the trip holding other things, like left-over food when traveling by train or gifts for friends which might get lost if loose in the backpack or suitcase.

I do not see any difference in how I handle laundry in my luggage between traveling with a back-pack, with a suitcase. Nor in using hostels or staying in homes of friends.
When using hotels I tend to bring more and not do laundry while traveling. I have never been traveling hotels for more than 3 weeks though.

This might not fit with your 'one bag' requirement. But that is because I feel that just one container is not enough for dirty and clean laundry in a single case or pack.