Bleach damaged hair is highly porous, it often won't hold colour well. Permanent and demi permanent box dyes contain peroxide so if you use those you are compounding the damage. Best thing is to use a highly pigmented semi permanent and leave for several hours, these should have a conditioner base so are not damaging at all.

I semi permanent dye (La Riche Directions) my hair red-pink over three hours and the colour lasts months with conditioner only washing, cool water and 'sealing' in with coconut oil treatments. Actually far better than when I used a permanent box dye (Live XXL) which damaged my hair horribly with the six to eight week 'refresh' of the lengths.

Do be sure to do strand tests so you know if your lengths need less treatment time than the hair closer to the roots - porous hair can absorb semi permanent dye at an alarming rate.