I need some advice.

I've been dyeing my hair black for a year now and I'm getting bored with it.. I'd really love to dye my hair red. But not REDred, not like a really bright unnatural looking red, but a nice natural looking red. I know I have to bleach my hair before I can dye my hair, but when I bleach it, does my hair turn yellow? The thing is, I'm scared my hair will be too orangey after I've bleached and dyed it.. I mean, if my hair's yellow after I've bleached it, the red color isn't going to be very dark. Right? And I really don't want orange hair. So, do you guys think it would be possible to get a color like this? :