I'm a bit confused. Are you this person's boss? You said she was "with another participant". Does your work involve home visits with clients? I understand feeling resentment about someone else wasting your (my) time, but there are some jobs that interfere with being somewhere at a precise time.
I have a job that entails seeing clients in various locations. I find it almost impossible to keep a precise schedule under those circumstances. I tell people I will be at their location within a 30 minute window ( 15 minutes before/after) of the appointment time. If one appointment runs long, I could be late. If traffic is bad, I could be late. There are many things outside my control that can impact my arrival.
Maybe the next time you need to schedule an appointment with this person you could arrange to meet at your office first thing in the morning, before she starts seeing clients? It would also be a good idea to schedule a meeting to address her timeliness when you are not already upset about it. If it is a lack of planning/organization on her part, does your employer offer any kind of time management training?