Thanks, I've since bought a one-size-fits-all (Succi? brand) at REI. It turns out the helmet's snap-on bill can still snap into the fittings on the helmet -- through the cover. That's good, as I can still use the Bell rear-view mirror that fits into the bill. I can also pull up the back enough that the clip-on light fits on the strap in the back and probably helps hold the cover on. It all works!
I'm aware of the warnings about helmet materials deteriorating with age as the same is said about the liners in my motorcycle helmets. In that case, the usual recommendation is replacement in about 5 years. Sorry, but if the helmet is still in pretty good shape otherwise, I'll take my chances. :-)
And yes, a shower cap would work, but, ummm, no thanks. Bike helmets look dorky enough to begin with...