If I'm truthful, I've bleached my hair every colour of the rainbow, and now it is terribly dry and awful. If your only planning on bleaching it one time, it should be fine however use lots of conditioner to bring your hair back to it's natural condition.
I have stopped dying my hair for a while and letting it grow out, the last time it was pink at the front and it really killed my hair, luckily it is gone now and has been cut out, but honestly be really careful when doing something as extreme as this.
There are other ways to get colour in your hair without damaging it, hair extensions are widely available on the internet for streaks or bursts of colour, and these can be glued [with proper hair glue] or clipped in without damaging your hair at all.
If you are going to dye your hair a colour, I recommended 'Special Effects' hair dye, although it is hard to get hold of it lasts the longest I've ever had it, and if you can't get that then 'Stargazer' is a pretty decent choice too.
Hope it all works out! ~
Just to give you an idea :
These are hair extensions. They are glued in with hair glue, they last forever and do not damage your hair at all. The colour never fades or anything.
This is when my hair was dyed pink. It was in a pretty bad condition after that, but it lasted a good long time. That was 'Stargazer' magenta dye.
This is when the front of my hair was blue. It faded very quickly, I can't remember what dye it was >.< Some natural herbie type stuff. The condition of my hair was alright at this point.
Hair extensions again ^-^
And finally ~ the fringe is dyed green with the same brand of blue dye, and the rest is all hair extensions.