The submissive alpha female is a woman who is strong, confident, bold, and assertive in her life and her dealings with people in general—but who wants a dominant man in her life because she finds it sexually exciting to be dominated by a strong, powerful man. She might or might not be in a position of authority at work; but she has a personality and a level of competence such that she could be in such a position and command respect.
I think this is just one of those things where people have different language preferences. Some people here seem to prefer the term “dominant” or “high-dominance woman” to describe a very similar thing, and I seem to recall that The Boss once even suggested the abbreviation “Dd”—to suggest that even though the woman is dominant, her man is more dominant.
But I have an allergy to using the word “dominant” to describe a woman (and especially myself), much like many women here seem to be a little uncomfortable using the word “submissive”. So while I would say that an “alpha submissive” woman (or a “submissive alpha female”) is assertive and even aggressive when the situation demands it, I would not say that she is dominant. To me, the word “dominance” connotes power over others (or another)—whereas by the “alpha” prefix I meant more a power from within that does not really seek to dominate others but often ends up being in charge anyway.
I guess, really, I don't much like the word “dominate” used in any context other than the sexual one of male dominance and female submission. (Or maybe sports like boxing and wrestling, and also war—any activity that implies actual physical conquest of an opponent.) While I have been in positions of authority at work, I usually don't view it as a conflict where I'm trying to get control over another person. And I was never that way in sports, either, although I did martial arts for a few years and loved it.
So I tend to think of myself as a woman who is not submissive except sexually (that is, in a romantic relationship); and also as someone who is not really dominant in any context or circumstance. That is, I might find myself in positions where I need to exert some authority and I can do that; but I have never enjoyed dominating anyone, not even non-sexually.
Hmmmm. Well, OK, that may not be entirely true. Because I always enjoyed beating the boys in math; and I do enjoy winning a good debate. But once again, I don't really think of that as domination because it's not physical. I don't use the word “dominate” to describe intellectual endeavors. But apparently other people sometimes consider such behavior dominating or even domineering.
I always thought it would be fun to beat my man in an intense intellectual argument, and then have him get physical about it, and show me who's really the boss, and why. Sadly, however, that does not seem to be the response of most males when they find a female beating them in math or logic or etc. Instead, they seem to conclude that she enjoys dominating men, and so they either lose interest because of their wounded egos (if they're dominant) or else they start groveling and put her up on a pedestal (if they're submissive).
Where, oh where, is the man who understands that a woman who whips his butt in an intellectual argument might just be looking to get hers whipped by his strong, manly hands?