We found a place in Bishkek that sells Chinese food. I've been told there are a few more places that we'll have to check, but we bought brown sugar, cornstarch (I cannot figure out where it's been hiding in all the regular stores here; I know I bought it in Bishkek before), rice vinegar, and sesame oil. There were a bazillion different types of vinegar and I was hoping for a black rice vinegar, but I couldn't decide if I'd found one since all the bottles were labeled in Chinese, of course, with Russian explanations below. There was a Muslim vinegar (makes me curious, but I don't like seasoned vinegars, and I wasn't sure this wasn't) and various other dark-colored vinegars. Definitely taking the dictionary next time.
And I suppose I ought to post where the place is, since it was hard for me to track down the location by searching online. We went to Goin which is on the NE corner of Jibek Jolu and Soviet (the food is immediately on your right as you enter the building). Apparently there's another store there that sells food, but I only found the one. And then there's Taatan, which I haven't been to yet since it's not in a very convenient part of town. I think it's on Armavirskaya a little north of Frunze. It's on the east edge of Bishkek not far from Lebedinovka (village, not street). I hear there is coconut milk to be found in Bishkek, so we'll definitely visit Taatan.