Put bleach in the skimmer and acid in your pool, and you can do them both at the same time WITH THE PUMP RUNNING!

Chlorine math: 120,000 gal = ~ 1,000,000# water; 120/5 = pool factor of 24; 6% bleach => 8.6# x 0.06 = ~0.5 lbs Cl2 equiv; 24 x 0.5 = 12 ppm; 12/4 (1/4 gal) = 3 ppm

Acid math: seat of the pants. pH calcs are hard, even if you have accurate TA values, accurate knowledge of the various buffers present (polyprotic acids) and accurate initial pH values. Conservative seat of the pants measurements work OK.

Adding sodium bicarb now just means more acid later.