I recently bleached my hair blonde from a dyed black. I didn't like the way the blonde looked so I dyed my hair red. The roots are really red but the ends are more orangy blonde cause it was so dead from the bleach. Now I want to do my hair purple. Would it take over the faded out red-orange or will I have to bleach it again? I would like to do a real purple. I would NOT want to bleach it again and was wondering if anyone knows a good purple dye that will turn my hair purple.

And another thing,
Im sure the ends of my hair will be purple, but my question is, if I do it will my roots be a different color than my tips cause of the coloring I have now?. I want my hair to be the same color purple from roots so tip.