First, Mary is a metamour, not a tertiary. You're not dating Mary so she isn't primary/secondary/tertiary to you in any fashion.
Next, Mary has no obligation whatsoever to meet you and spend time with you. It is as simple as that. Whether or not the two of you meet has absolutely nothing to do with showing respect for the other's time with Beth.
Third, your reaction to going to the same bar they were scheduled to arrive at later is entirely your problem. You could have stayed there and enjoyed yourself--you had no obligation to leave just because Mary doesn't want to run into you. Piss on that--you don't have to schedule your life around her desire to not meet you. How 'bout you stop worrying about that and schedule your free time without giving her a single thought? Life will be much better that way.
When speaking of various forms of non-monogamy...it ain't poly if you're just fucking around.
While polyamory, open relationships, and swinging are all distinctly different approaches to non-monogamy, they are not mutually exlusive. Folks can, and some do, engage in more than one of them at a time--and it's all good.