You know that 手洗い is "handwashing" (and also a not as polite way to mention a bathroom). When you add お you're suddenly making it polite. Why? Because you're talking about something a little more crass than handwashing. You're talking about the toilet or restroom or bathroom. Ewww. Poop goes there.
The reading comes from 手洗い, so if you know that you'll know this too!