This is a serious problem to have, and it is probably a good idea to memorize a few places you can reliably find one before you get stuck in a really rough situation.
Luckily, as long as you are near businesses, you can usually find somewhere nearby. Most bars will let people come in just to take a quick trip to the bathroom, but this won't work everywhere. Grocery stores are often a good place, along with libraries and some public parks. Day programs and any shelter space that is open 24 hours have bathrooms too.
Downtown Portland is usually the easiest place to find a place to piss, but we will try to include locations across the metro area. If you can't find somewhere, as long as no one sees you, no one will care if you go outside. Just find somewhere as hidden as possible. Being homeless is rarely a dignifying and pleasant experience, but everyone out here learns to manage it somehow.
Here is a map of bathroom locations. If you know of a place that is not currently listed, send it to e5036260119@gmail.com or use the feedback form at the bottom of the page.