Help with hair gradient?

So it's been about 2 years since I last dyed my hair bright colours and I seriously miss it.

The first photo is my hair now, I've been trying to grow out my blonde for a natural ombre look so my roots are quite prominent. maybe 2-3 inches? regrowth colour is a light mouse brown, and my hair gradually lightens up through a medium to a light dirty blonde.

I really don't want to bleach my roots because I'd quite like to grow it out further, and I was thinking of possibly dying it blue or purple, darkish fading out to light like my hair is now.

(2nd photo) I absolutely adore this shade of purple and would probably like this to be the lightest colour (any reccomendations would be fab!), gradually getting darker towards the roots. but how should I tackle my roots? Do you think any purples will show up without looking too dirty? I don't mind lightening the ends of my hair to get a nicer light purple, but I really don't want to touch my roots with any bleach.

(3rd photo) I also adore Lua's red ombre, and I imagine red will work better with my dark roots, but red is such a pain to get out again :p

Edit: also my hair is just to the top of my boob, so not SUPER long...