Do I have to bleach my hair before dying it blue?

My natural hair color is a dirty blond, but I've dyed it brown for almost a year. By now, he brown has grown out of it mostly, but I didn't want to go back to my natural color (since it doesn't look very good) and dyed it a light blond.

I would like to dye parts of my hair blue next month, using one of the Manic Panic colors. I'm a little worried about bleaching my hair since it's such an aggressive method and my skin is rather sensitive. The brand of hair dye I'm using right now works well for me, but other products have started to really hurt me a couple of minutes after putting them in my hair (even though I did the allergy test two days earlier and had no suspicious reaction whatsoever). However, while there is no bleaching product available of the same brand, they have some very light almost-bleached blonde tones.

Could I use those or would my hair (after putting on the blue) turn green, since bleaching involves a different process than simply dying it?

I was also thinking about trying to bleach just a small section of my hair first, so I wouldn't do much damage in case it should fall off or anything. If that works well, would it consequently work well for the rest of my hair too, or could the higher "dose" of bleaching product still cause harm?