Purple Blue ombre?

I'm not the best person to advise you about bleaching the roots as it's something I've never done 🙂 but you can tease your hair a bit before applying the hairdye, this way you won't have a straight line and it will look like the two colors blend one into the other in a more natural way.

That doesn't really work with a gradient this way around.

Just bleach your roots like normal, it should be fine. There's two ways of avoiding a bright line. One is pick a deeper purple. The other is to first dye the roots the same blue as the rest.

I've done gradients several times now. I put the colour at the roots first, then I literally just pull it through to the level I want it. That way it gets a nice broken soft line. If then you want to top up the blue, start putting it on the ends, a few centimetres below where you want it to blend with the purple. The again start pulling the blue to the ends, starting at the end of the purple. There should be enough blue on your gloves to gradually start blending it. If you need more dye, just gradually add more.

It's time consuming, but it's the most effective way 🙂