I bleach my hair a fair amount because i like having funky colours and i also like being blonde between dyes. I have pretty thick 2c/3a hair.
For me it doesnt damage my hair all that much. I just make sure it's in the best condition first ie i'll deep condition it and then after it is bleached i condition my hair a lot i also deep condition and i wont bleach it for at least 2 months which is about the time my roots are starting to look appauling.
If you have pretty thick, strong hair then it wont do too much damage. Just condition it lots and get the dead ends cut off.