And I found a way to fix it! I finished off a Method bottle of fabric softener and got to work cleaning it out. Once it was clean and dry, I poured the rest of my latest bottle of Clorox into it.
And, ta DA! A clean, pump-happy bleach bottle.
Seriously, I love it. I love that it's easy to use. I love that it was free, and solved a problem. So, I'm sharing my idea, and hoping it can solve anyone else's OCD problem with bleach bottles too!
Happy cleaning y'all!