The earliest Christians in Rome most likely belonged to the circle of the Synagogue, mostly from among the 'god-fearing' Gentiles (and even if we assume that Mary Magdalene was very young at the time she met Jesus - age 14 would be enough for her to be referred to as a 'woman' - in order for her to be a useful leader she would have to be in the earliest years of the Christian community in Rome). Many of these people would not have too much of a problem acknowledging a woman as a religious leader (it was, after all, common in other religious groups of the time as well as other Christian communities in the Hellenistic world). As an eyewitness with close ties with Jesus (just how close may be a subject of debate even at the time) she would certainly be able to command the kind of respect required. As to 'bishop', the formal position wouldn't even exist yet, so a better term would be 'community leader'. Yes, Paul speaks of 'episkopoi', but that's much closer to 'Elders' or 'preachers' than what we understand by a bishop.
It might lead to a stronger and earlier separation of the Christian community in Rome from the Jews. I doubt the synagogue would be as forgiving of a female leader. If she writes down stuff, of course, we have a pretty good chance of it surviving, given her exposed position and great prominence. Or maybe not - I hate to say it, but this may terminally damage the credibility of the new religion with the Roman upper classes. Which makes a strong incentive not to talk about this.
For all we know, she might have been.
Oh, and regarding 'Pope Joan': it allegedly happened in the 9th century, and while I personally doubt the veracity of the story (it is too useful as a propaganda tool) there's very little that wasn't possible in the Lateran at the time.