You should always be using gloves when handling an irritant such as bleach.
Wash any skin immediately after exposure with plenty of water - truly flush the area to remove any traces of bleach and stop the reaction. I would not recommend using soap on a fresh chemical burn as it would irritate the wound and sting like the bejesus (ever gotten soap in a fresh cut?). Then give the skin a few days to heal, avoiding soap while the wound is still throbbing if you can, and avoid using perfumed products such as moisturisers or other cosmetics near the burn. You may benefit from using a dab of antiseptic such as Savlon or using a burn cream such as Bepanthen. Keep your fingers clean and don't go dipping your fingertips on anything that is likely to harbour a lot of bacteria. And next time, learn your lesson and use gloves. Continued burns from bleach can cause you to develop an allergic reaction to it, so do a patch test on unbroken skin before the next time you bleach your roots (and please follow the same principles for bleaching your roots, avoid getting bleach on your scalp if at all possible and do not leave it there to burn if you get some on your hairline or ears. Wipe it off immediately with a dampened cloth.)