Okay, I'm worried about the direction this whole discussion took. Here's why: the comment came up as the appointment was finishing, so, Girl, you were left with no opportunity to sift through your own thoughts/feelings before having to leave. (Leaving in confusion is the worst thing, for me, personally. I lose heart so quickly.) Not only are you already uncomfortable about not being able to be at the appointment when you want to be but are, instead, at the mercy of the mass transit schedule, but you also have this nagging echo from your past that says that people who are late for appointments with you don't care enough about you to be on time (i.e., that you're not important--or not as important as someone else or blah, blah, blah, who-knows-what-it-is-but-it's-something-at-least-a-little-heartbreaking). Then, there's the fact that early therapy appointments are stressful in terms of building a relationship--or worrying about whether or not we have one.
So, holy-moly . . . . . . it's all this anxiety and fear and shame and indignation at being misunderstood and this wish to be treated fairly and with attention to the facts and to our feelings so that all the whole $hitload of everything that's always happened before doesn't happen again now, here, with this Very Important Person. Well . . . . . it's just exhausting and makes a person feel defeated.
So, here's what I think: the good news is that it DID come up at the end of a session and you had to go away instead of get all tangled up into a finely tuned analysis of something that isn't, actually, going to change (probably. I mean, you still will take the bus, she is still probably over-extended and learning how to manage her own time and her own schedule . . . people can get pretty complicated schedules going if they don't spend their whole day in one office seeing patients there). So, now, at this point, you get to say, well . . . The Facts: I ride the bus. I get there early. It'll be nice when she gets used to that fact and stops being uncomfortable with it. And you get to say: I'm glad she's not borderline, like me, and doesn't get pissed off about this kind of stuff. I wonder if she is irritated? And really, I wonder if it's that she's irritated that I'm early or that she senses that I'm irritated that she's late? And, also, you get to say this: I wonder what it will be like for the two of us to get used to each other's schedules--me too early, her a little late?

And, finally, I think it's really, really important for us all to separate out the being early because that's the logistical arrangement you have to make to be there at the start of your appointment time from the emotional reactions to late/early anxiety over respect/pushy/needy/cavalier and so on. The fact is, it's probably true that Girl has to be there early in order to be on time for her appointment. But that is the really, really interesting question that you get to ask now, and it goes like this:
Girl to therapist: "You said I should try being late. I worried about that a little. If I were late . . . would that mean that I would still have to leave at the end of the hour, or would you be able to have enough time at the scheduled end of the appointment to tack a little time on?" You could even ask: "Is this a good time of day to have the appointments? It seems to be hard for you to get here on time, and I have to get here early. Is there another option that would work better? It's okay, it there isn't, but what do you think?"
And that question-asking, and choice making, and taking responsibility without blame (and also without hurting yourself--as in denying yourself comfort and cheer because you must be wrong and they must be right) that's what DBT and therapy and our constant self-work is all about. IMO.