What should I cover bread dough with while it's rising?

A good alternative to either a towel (which you have to wash and is prone to sticking) or plastic wrap (which ain't cheap or good for the environment) is a clear plastic shower cap. It does the same job as plastic wrap, but is reusable. The elasticated edge stretches around even big bowls, providing a snug fit.

Personally, I spray plastic wrap with oil, then use that. Doesn't stick, even with very high hydration doughs, and completely prevents the dough from drying.

Another method is to use a food-grade plastic bag. Tie it shut inflated with air (so it isn't touching the dough). The humidity in the bag will stay high enough to prevent drying, and since the dough doesn't touch the bag, the bag stays clean and can be re-used.

The food-safe bag is the most environmentally friendly (washing cloths isn't so environmentally friendly).

Put a serving plate over the bowl. Normal way up so it doesn't slide off and doesn't need washing. Easy!

A small amount of surface drying is not going to ruin a bread dough. Think of the millions of bread making machines out there, no plastic wrap required with them, just a reasonably fitting lid that stops air drafts, hence why the towel method worked fine

I work with quite wet doughs and bake in a moist environment, but

first rise - in a large Tupperware container, lid on but ajar at a corner to let gases escape.

second rise - simply dusted with flour.

No noticeable skinning at all or loss of oven spring.

I just put a sheet of baking paper on top of the mixing bowl (in which I mixed the dough) and rest a wooden cutting board (which I used to knead the dough). I'll use the baking paper in the baking tin later, so nothing got wasted and there's no extra mess :)

I've been letting my pizza dough rise in reusable plastic containers with plastic lids (I coat the bottom and sides of the containers with a bit of olive oil so that the dough doesn't stick). Seems to work just fine, and it's incredibly easy.

I use shower caps especially kept for this purpose and just lightly oil the inside of them. Either normal ones or the thin, clear sort you get in hotels work fine and saves the hassle and waste of clingfilm.

I prefer not to introduce plastic into my baking where feasible. I spend time and money and love on baking, using nice organic flours and all natural ingedients, and the plastic shower cap, although very effective, makes me think there are unhealthy hydrocarbons dripping on to the lovely dough. I vote for clean white flour sack lint free tea towels, dampened aNd even re dampened if needed. I like the dinner plate over the bowl technique too.