In my experience, Aglaonemas tend to be fairly resistant to mites, so this isn't as bad as it looks.

What I would do is, I'd get a paper towel, squeeze a little dishwashing liquid on it, wet it down with WARM (not hot or cold) water, and then wipe all the leaves top and bottom with the towel. Do the same thing again in a few days. If your weather forecast for the next week or so is for temperatures above 60F (including at night), I'd put it outside in a sheltered, shady spot too, but if you're expecting cold, or don't have a place to put it, or etc., then you can leave it inside.

Spider mites are fairly predictable: they have certain plants they prefer to eat, and certain conditions they like. Change any part of the equation and you can discourage them. Their preferred plants are, more or less:

Codiaeum variegatum (croton)
Hedera helix, H. canariensis (English ivy, Algerian ivy)
Schefflera actinophylla and S. arboricola (umbrella tree)
Dizygotheca elegantissima (false aralia, now technically Schefflera elegantissima)
Cissus rhombifolia (grape ivy)
Ficus spp. (ficus tree, rubber plant, fiddle-leaf fig, long-leaf fig, Alii fig)
Musa spp. (banana)
Maranta spp., Calathea spp. (prayer plant)
Cordyline terminalis (ti plant)

If you have any of these other plants, you should check it, because the odds are good that it's got them too.

They also like hot, dry conditions, with stagnant air. Raising the humidity will deter them, as will running a fan in the room or moving plants away from walls and corners. (This is why I recommend outside: outside is almost always more humid, and almost always has better airflow.) I wouldn't advise trying to cool the room so much, at least not necessarily, because Aglaonemas are touchy about cold, and can be damaged at or below about 60F. Some of the new varieties are more cold-resistant, but I don't know about 'Silver Bay' specifically.

Leaves that have discolored won't come back; you may be able to save yourself some work by pulling off a few of the leaves with the biggest mite populations.

But really, this isn't anything to panic about; it's one of the easier pest combinations I can think of. If it should persist after a couple wipedowns with soapy water, then you could look into neem oil, which I'm fairly certain is nontoxic to people and birds. Though it smells kinda funny.

Well, the soap seems to be working! I took the plant outside, and instead of simply "wiping" all the leaves (since there are so many) I dunked them each in a bowl of soapy water. THEN I wiped them quickly with a cotton make-up sponge. The loose cotton really grabbed all the left-over mites. It's been 24 hours and I still can't find any roaming mites. I'm keeping the plant isolated for now and hoping the coming humidity will discourage them some more. I guess I'll re-treat sometime next week.

But, is it possible to completely get rid of them? Or do they just barely get by until late spring when conditions are ripe and then flare up in droves?

It's possible to completely get rid of them, but any time you bring in a new plant from somewhere, you run the risk of introducing a new mite population. Even if plants never actually touch one another, mites are small enough and light enough that they can float some distance through the air, or hitch a ride on your hand from one plant to the next, and it only takes one pregnant female. The question is not so much, will they come back, as it is, why aren't they a huge issue all the time?

The good news is, they can be lived with, to a degree, and if you've got good air circulation and humidity, if you clean the plant regularly (or even just stick it in the shower to water sometimes), and if you learn to recognize the early signs of infestation, you can go for quite a while without having any serious problems.

I've only lost a handful of plants to spider mites, even with all the plants that have come in and out of my home (something like 500-600 over the last few years): I lose maybe three times more to watering problems, either too much or too little, than I do to pests.

Given the option to eliminate one houseplant pest from the world forever, spider mites would be my third choice, after mealybugs and scale. They're bad, but they're not terrifying.