Transitioning from tweezing to bleaching mustache hairs

I (f) stopped tweezing about a month ago and started bleaching a week or week and a half ago. The first day after initially bleaching was perfect, no hairs visible. But by the second day I noticed black roots already. I did a touch up a few days later and same thing: first day good, after second day, more and more black roots everywhere.

My hair grows fast generally. Does this mean bleaching will not be an option for me? I don't like seeing the black roots. Or will the growth rate slow down once my hairs grow to their full length, after recovering from the tweezing, I guess?

I would love to hear from anybody's experience! and/or advice! thanks :)