Orangey hair

My hair hasn't faded orangey the same as it normally does; it's gone a darker red that almost resemled "dark pink" for a while (grey-y red).

I'm wondering, since so many people get orange hair attempted to go blonde, how hard is it to do? My hair is currently dyed red sort of faded, and I want to go for a "natural" red, but brighter.

I'm not sure I trust myself with bleach, although I know that it usual comes from when people attempt to use blonde dye, but I'd feel silly doing the wrong colour and the results are unpredictable.
I've seen a lot of people dye their hair lightish orange-red from fairly dark colours; moreso than most colours.

My hair has been dyed quite a bit previously but is thick and strong and should be fine.

I think I'm dying it tomorrow, so if anyone sees this before then, it'd be much appreciated.