I've never done Bok-Choi but I would think 2-4 weeks tops. Remember, they can be planted out anytime after first true leaves. And if you're worried about frost, just use floating row cover, or if you don't have any, any lightweight fabric if they are calling for frost, or heck, newspapers.
I usually start my Chinese cabbage the same time as broccoli, etc. and it's always done fine. My biggest problem is keeping that floating row cover on and not getting swiss cheese leaves! I have one customer who always comments on that, but jokes he know's I grow organically, and he always buys it! I so want some without holes for him this spring!
