question about bleaching.

I’ve done plenty of research about upperlip hair removal to see what my options are. As a girl struggling to pay college tuition, I can’t really afford the lasers. I’m considering bleaching. Does anyone know much about this topic? I’m asian, dark haired and I’ll describe my skin tone as … “beige” or like a light brown. I have peach fuzz on my upperlip, the kind that’s not really noticeable until you look for it. It isn’t growing out of control or very very dark. Bleaching sounds good because its cheap and accessible (5 dollars at a drug store) but I hear horror stories about how it lightens your skin tone. In my case, since its just fuzz, i dont think I’ll have to use it too often… but how often is too often and your skin becomes bleached in the process?