Derek,
I too frequent a cafe that has a bathroom with a lidless, small trash can. Although I'm not fully incontinent, I use diapers along with Pull-ups to manage my O.A.B. & light incontinence. During stressful or anxious periods of time, leaking becomes both heavy and constant, so I switch to diapers. I've been at the cafe working on my lap top during these times and have had to change, even more than once, without a proper to trashcan to dispose of the used diapers. This may sound gross, but depending on what kind of accidents you are having, you can bring zip lock bags and bring your used diapers along with you in your bag after changing, until you can throw them away in a more discreet can.
This is what I do, but I am only dealing with wet diapers. I've used this method while staying at peoples houses and even work days.