Bleaching black hair?

I have very black hair. My natural color is dark brown. It's been dyed about 6 times in the past 2 years. (the most recent dye job was 1.5 months ago) I want to add blue to my hair. Not my whole head, just the top of my bangs and sides. In order to achieve the right shade of blue, how many times will I have to bleach my hair? I can not afford to go to a salon, I'm just going to use those $10 box kits from the drug store. It needs to be blonde first in order for the blue to even show up. Thanks in advance! :)