This is a difficult situation for both male ostomates and female ostomates. The average public has no idea what these operations are and when you have to explain to them what they are, and that you have one, many of them recoil in shocked horror and look at you like you have three heads. I've gotten "unlucky" a number of times when I was on the verge of victory only to have to mention this um...little inconvenience.
I have found that nurses, nurse aides, doctors, and other medical technicians are not fazed by this situation. I think probably some lawyers and other professional people also are intelligent enough not to be struck dumb with terror upon having the situation explained to them.
The other option, is of course, to find a fellow Ostomate. At least you don't have to go through a complicated potentially humiliating dramatic scene with your potential girl/boyfriend about what the situation is, what it means, and how we have to live with it.