You are on your way!

However, while Tri-chlor pucks and Di-Chlor powder will lower your pH noticeably when you chlorinate with them, Bleach will not raise pH noticeably.

While Bleach is a high-pH item, you can generally act as if it's neutral when adding it to your water. Borax is FAR more effective at raising pH.

So you should be testing your water all the time anyway, so you can stay ahead of changes in pH that you don't like.