What's the least damaging way to bleach roots?

Bleaching any part of your hair automatically means damage, so the least damaging way to bleach your roots is to not bleach them at all (haha bad joke :P)

Using the lowest volume bleach will minimize the damage (at least in my experience). So if you've got blond hair already, you'll probably only need a 20vol or even a 10 if you're pretty close to platinum blond already. Darker hair needs 30vol (that's what I used, I'm medium brunette), and black hair takes 40vol but you have to be careful with that because it burns your scalp.

2nd tip: only bleach as light as your color requires. I use a lot of really dark colors, so I tend not to need to bleach all the way white because my color will take anyway and cover up any brassiness. If you're going orange or red, the same thing applies- brassiness may not show as much because the dye is similar to the base tone. Colors like turquoise or pastels require basically white hair, and thus more damage, for a true color that isn't muddy.

3rd: I'm sure you've heard this before, but do a strand test! Check out the quality of the bleached bit, how light it went, if you're happy with that color with that amount of damage. Also, conditioner well after bleaching, even leave your roots a couple of days after bleaching but before dyeing so you can give your hair a break and really condition it well.

Hope this helps :)

I find that as the roots are virgin hair the lower volumes of peroxide work fine. I recently did my root re-growth with 20vol and they came out white and my roots are very dark brown/almost black, So i suggest lower volumes first before jumping straight into 30/40 hope that helps :)

As above, lower volume of peroxide. Also bleaching it in two parts can help; the heat from your scalp can speed up the processing time of the bleach, so if you don't work quick enough the section you started on will be light enough while you're still waiting on the section you finished with to get light enough. So that way if you only bleach half your head at once you won't be over processing any sections.

Also try bleaching when your hair is oily so the scalp isn't as irritated.