Usually I poop before I leave for work, so I don't have to there. But sometimes I have to go right after I get to work or other random times during the day.
The nice thing is, at my work, there is a third, separate restroom that only has a toilet and a sink, and a locking door. So if I have to poop, I go in that one and have complete privacy. The only time I use the other restroom is if somebody's in that one, and usually it's just to pee.
As for public restrooms, I like the ones at Lowes and Home Depot best because they have like 10 stalls, so you can easily go in there and nobody would even know you were there. Walmart is kinda like that too but they get way too many people coming in and out and it makes me nervous, so I avoid those.
One funny story, once I was in the restroom at work in the stall, and somebody came in and when they left they turned the lights off. I was too nervous to yell out at them. So I was in pitch dark trying to get out and turn the lights back on before anybody else came in. Because that would be weird for somebody to come in and I'm in the restroom with the lights off. Fortunately I was able to though.