No, she doesn't need to drain any water. She has algae simply because she has no chlorine in her pool. Even though she has added some bleach, without having any cya in there, the chlorine isn't going to stick around long especially if it is hot and sunny.

For now, she needs to test her water at least 2x a day (and 3x a day would be better) and each time, add enough bleach to get her chlorine reading back up to 8-10. This is the only way to kill algae -- to sustain a high chlorine level. If it yo-yos up and down, she'll never defeat it. Also, run the pump 24/7 while trying to clear the water.

After the water clears, then she'll need to add some cya. Add enough per label directions to get a reading of about 25 ppm for now. She can add it directly into the skimmer while the pump is running. It will take up to a week to dissolve in the filter, so during that time, she shouldn't retest for it nor add any more. Don't want to overshoot the target. It is easier to add a little more later if needed, but if you get too much in there, the only way to reduce it is to do a partial drain. Until the cya begins to dissolve, her chlorine will disappear pretty quick so she'll need to continue testing at least 2x a day so the algae won't return. After the cya begins to show up, she'll be able to just test and dose with bleach in the evenings only. Hope this helps.

PH, alk and calcium all look fine.