How can i prevent hair breakage when bleaching my hair?

i've been dying my hair for about two years now, but recently when i bleach my hair, it literally falls off. not all of it, but at least an inch. Is there any way i can prevent this? I REALLY want to dye my hair blue in april. but if it means losing an inch of hair, when im trying to grow it out, it wouldnt be worth it.