Tips for dying my underlayer?

I want to dye my underlayer purple but I’m not entirely sure how. I know the basics. Pin up the majority of the hair and leave down the layer I want to dye. Do I apply the dye all the way to the roots of the underlayer though or only at the tips? How high up? I’m doing my bangs to so any tips you have for that will be helpful. Plus I haven’t decided yet if I want to dye all of my bangs or just the underlayer of them, what is your personal preference?

Also! If you have any suggestions for hair dye I could use. I want a deep purple, something that will last a while. I have naturally dark brown hair that’s recently been died dark brown from a light brownish red. Thank you.