The best thing to do is to visit a good hairdresser and ask for their advice. Personally, I don't like to use bleach since it's too chemically for my likings and gives hair a bristly look.

Darker hair doesn't really take on color (most semi-permanent color dyes) very well, even if the color is just as dark as your hair. My hair color is light brown and I have it dyed black and red, but when I don't bleach it before I dye it red it only stays for about a week (rather than at least four) and then turns brown again instead of fading normally.
Alternatively, if you can find a permanent haircolor kit that includes a bleaching agent in it like most permanent natural color dyes do, you don't need to bleach and it's probably easier on your hair. I've never seen these in purple though.
If you do bleach, even though your hair is dark, make sure you don't leave the bleach in too long or your hair will be sad and unhealthy.