Is your work near any shops, etc.? Other office buildings? Perhaps you could find a more private bathroom somewhere close by. Even if it's another office building - if you act like you know what you're doing you can generally walk right into any place, so long as they don't have actual security.
At my work we have a bathroom in our main building and we used to have a second building with a very private bathroom, but it recently burned down.
Now, the only bathroom left is right in the main area where everyone is. It's a one person bathroom, and sometimes people will even wait outside if it's occupied (why??). Noise and smell travel easily, so if someone poops it is well known. I can generally hold it in until I get home, but if I can't I'll drive to a department store that has nice facilities.
You have to know where to look for good bathrooms. Department stores (Macy's, Sears, etc.) are usually really good. Office supply stores like Staples have clean rest rooms. Office buildings, especially one's that rent to doctors. Hospitals can be good. Universities always have some great out of the way bathrooms that are hardly used.