Water is also a good protector. And the polyethylene is actually a proxy for "hydrogen atoms". The reason is that dense hydrogen has a lot of protons to interact with the incoming radiation.

But unfortunately plastic bags are not dense polyethylene. You would kind of need full blocks of solid polyethylene...

You can make solid polyethylene out of plastic bags by pressing them in a mold heated to ~100-150C.

But it's quite flammable, so you might not want to use it as a building material.

The peer comment posted a source that has lots of references.

Though most of them are tests in space, where I assume the thickness requirements would rule out grocery bags. I am curious how thick a layer of HDPE you would need on earth to make any notable difference.

That linked nature paper seems to indicate 10g/cm^2 for a 50% reduction. A standard shopping bag is about 5g, so you would need roughly 20k bags/m^2, or ~2k bags/ft^2. At 0.9g/cm^3, that would be roughly 11cm of solid polyethylene

I just squished a plastic bag as much as I could, and got it down to an inch cubed. So if I hypothetically did that for 2000 bags in 1ft^2 (sorry for English units), I think that would mean it could be 13-14in thick. So maybe it is reasonable to attenuate radiation by about 50% in a rather generous drop ceiling?

Ah, so bags are out, as is practically the ceiling. But cut sheet HDPE is easy to find, so tiles atop your machine would be relatively cheap and easy.

I work for a particle accelerator, and I can confirm you that our beam dump uses polyethylene for neutron shielding: https://www.sciencedirect.com/science/article/pii/S092037961...

Doesn't sound like that solution is plenum-rated.