Bleach (and chlorinating liquid) do raise the pH when you add them, but the usage of the chlorine lowers the pH so it's really pH neutral. Don't try to add acid after adding bleach in order to get the pH just right. You'll yo-yo back and forth. Measure your pH consistently, just before you add more chlorine. Finally, if you have enough TA, the addition of chlorine will only raise the pH by about 0.1 to 0.2 which isn't very much. If you measure your pH before you add chlorine, you can target 7.4 and then after chlorine addition it will be 7.5-7.6 and will then slowly drift back down to 7.4 the next time you add chlorine.

The above scenario assumes you aren't experiencing a general rise in pH. Most pools have that and it has nothing to do with the chlorine, but rather the outgassing of carbon dioxide from your pool. Having a lower TA (say, 80 ppm) helps reduce this problem.

Richard