This is a kind of long response. But I hope maybe you'll read through it. Just saying "check your privilege" is probably not the best starting point for the conversation, so I'll try to do a better job of explaining. I don't know if you are misunderstanding what is meant by "privilege" or not, but the privilege being talked about when someone says "check your privilege" in my experience are the privileges that come from being part of the, for lack of a better term, more socially accepted or socially powerful group. Things like white privilege, male privilege, heterosexual privilege, you get the idea.
So regardless of your level of income or education, you can be, and probably are, still privileged in the way society sees and treats you.
For example, as a man, I pretty much never have to worry about being told I got a promotion because I was having sex with the boss, or that I'm only being angry or "emotional" about something because it's my "time of the month". Things that women have to deal with all the time.
Another example would be that I'm never worried wanting to have children is going to be seen as bad for business, and result in me being denied promotions or other advancement because of it.(Not to mention I'm statistically going to be getting paid more than women for doing equal work.)
Hopefully you can see how these are the type of privileges men, or another group of people in a similar situation, may never notice unless it is pointed out to them. Or they "check their privilege".
In relation to Ban Bossy, an important example seems to be that I've been conditioned my entire life to aspire to be a leader: team captain, salesman of the year, best on the basketball court, you get the idea. And not once was I ever, or will I ever, be discouraged from asserting my leadership skills as essentially "not knowing my place" because I'm a man, which can be the outcome when we tell girls and young women to not be bossy or other similar things.
Maybe a good exercise for you, and for all of us, is to listen to what people are saying when they describe the privileges we have, or to ask them to explain better because we would like to understand. Depending on our situation, maybe we'll gain a better understanding of our heterosexual privilege and being able to love who we want without having to worry that their gender will result in violence against us or them. Or maybe we'll learn about our religious privilege, and that we are able to practice a religion without inciting fear, being called names, profiled, assaulted, or killed because of the head covering we wear or for being "different".