dying straight onto ginger hair

Heyy!

I want to have small rainbow highlights in my hair, but I don't want the rainbow to be too obvious, and my hair is naturally ginger. Is it possible for me to get my natural hair dyed without bleach, or will it turn green like in everyones nightmares?? I'm scared! I've never dyed my hair before! I also don't mind if it becomes warm-toned.. thats kind of what I'm looking for!

Thanks :]