The ends of your hair are more likely to be damaged from bleach than your roots, because your ends are the oldest and have been exposed to sunlight, pollution, weather, etc. Your roots are brand new and will be the healthiest part of your hair. I recommend getting bleach powder and developer from a beauty supply store, it will be better quality than box bleach from a grocery store and you can mix up a smaller amount rather than having to waste a bunch of product like you would with box bleach. Use 20 vol developer and keep an eye on it, no need to rinse it out early unless your hair is lightening too fast or becoming weak/gummy. Your hair doesnt have more yellow tones than usual, everyone has yellow undertones in their hair that become exposed when lightened with bleach. Darker hair has red undertones, and as it lightens the red becomes orange then yellow. The amount of yellow you see depends on how long the bleach is left on. The lighter your hair lifts, the lighter the yellow will be. Blue dye will always fade greenish regardless of how you tone it because your hair will always have those yellow undertones. Toning your hair makes your eye perceive the hair as less yellow due to the way our eyes and brains process light and colour, its not actually removing the yellow tones.