You can work on pH and add bleach at the same time with no problem. Add a box of 20 Mule Team Borax (laundry aisle at Walmart) slowly to the skimmer while the pump is running, breaking up any clumps. Retest pH after a couple of hours and redose as needed until you get the pH between 7.4-7.6 (although anyplace 7.2-7.8 is ok).

Keep your chlorine at shock level while you are trying to clear up the green. Shock level is based upon your CYA reading. Take a look at the Best Guess Chlorine Chart in my signature below. Run your pump 24/7 while you are working to clear the pool. Keep an eye on your filter pressure and backwash when you see an 8-10psi rise over clean filter pressure.