Not sure I can answer, but must need some sun to grow properly, but 3 good hours it would at least grow. The main problem would be the heat since fast growing Bok Choy bolts easier than the "western" Brassicas. I would think the timing of the planting would be the most important. When would you try to grow it ideally in Texas?

There are sites that say you need hardly any sun to grow it properly, and that it can do fine with mostly reflected and ambient light.

http://reclaimgrowsustain.com/content/vegetables-you-can-grow-shade

But there are others that suggest you need more sunlight. Experience, anyone?

I'd put it in in a month or two. It's frost tolerant enough for here. Timing of the planting is mainly to avoid overheating and bolting.

In hot summer climates, it requires minimal sunlight and more shade than sun is suggested to prevent too rapid bolting. If growing for a winter crop, more sunlight is desired just due to the lower sun intensity and the fact that cooler fall and winter temps reduce bolting.

This is a very popular winter crop in my area, even commercially. And 3 hours of sunlight in late fall or winter here would be considered a gift!! If you count overcast days as no direct sunlight, bok choi grows perfectly well with almost no sun :-) But it is slow to mature.

Thanks. That makes some sense. Sounds like it'll work in my low-sun bed, but it'll just take time. I'm up for that.