Ladies have the advantage that they easily can carry a small diaper in a medium-size handbag very discreetly. Some have mentioned that it is convenient to carry a lighter-absorbency diaper than they usually wear - just enough to last until they can return home or have an opportunity to change into a heavy-duty diaper.
During those periods when I think I will be at high risk of an accident, I carry a small backpack. However, in many social situations that would attract attention and unwanted comments or questions.
Of course, I have a full "disaster kit" in my car - just in case.
--John
(double incontinent)