Using heat will make your developer break down too fast. You need to allow the product to stay on the hair (without heat) for a longer amount of time so that it can get right into the cortex and get at all that dark pigment, otherwise you are really just bleaching the cuticle and making the hair porous.
Mixing the bleach correctly, saturating the with enough product (not taking too thick highlights) and developing the hair slowly will all impact on how light you will get the hair, but if she has a build up of colour this may be a long term plan.