For the enthusiasts or followers of the practice of greeting friends by giving a "bise" it's been a tradition for at least the past 50 years to abide by the "friend of yours is a friend of mine" rule or some other rule that remains unacknowledged, and so is common the distribution of kisses to all present in a group where at least one person is by force of precedents entitled to that privilege; often, the custom is not that of giving just one "bise" but instead two, one on each cheek, or even three, four or five, changing from cheek to cheek for each new kiss in the series — it's complicated; however, let's make things quite clear: it's not a practice you'll witness in any group of persons knowing one another ; as years went on this behaviour has been extended to new types of groups but initially it was found among the young, the adolescents, and I suspect that even before its generalisation to groups comprising both boys and girls it was restricted to groups of girls or to the girls in the mixed groups. Typical groups are those of school friends, those of people participating together in sports events, groups of young people partying; for instance, that practice does not impinge upon groups based essentially on family ties: a stranger in such a group will not be sollicited to do that because no such custom exists for those groups.
So, if you happen to be in such a "bise" group, and know not at all a person suddenly joining it, whether that person is a male or a female, if he/she knows someone closely enough for this sort of greetings, you can expect that you also will be greeted that way, nevertheless only after at least one of those in the group for whom this is usual has been kissed; this priority principle, as it is in harmony with the principle that, roughly, bonds of camaraderie are reasserted first with those who enjoy a greater seniority in someone's frienship, serves at the same time the necessity of not being too intrusive upon a total stranger and, so to speak, in preparing them to a ritual that will appear more natural; there is almost never any hesitation on the part of the persons in such situations, neither from the kiss giver nor from the receiver, no soul searching as to the legitimacy of the act, no squeamishness. It was said above that one cannot be certain as to what really motivates this practice; the rather coldly reasoned attitude based on the "transitivity" of friendship is only a vague possibility. The practice can be seen as confering, apparently, feelings of great frienship and those given to the practice of greeting their friends with kisses may have feelings of guilt in the sense of having an impression that a discriminatory behaviour towards those they should treat differently, more formally, could be interpreted in a negative way. The practice could thus have sprung from an egalitarian concern. One must not forget either the easiness with which such acts of greeting can be performed: there is nothing to say and most of the time no verbal exchange will accompany them; it's done rapidly and you can go on quickly to someone else to whom you don't really have anything to say. Therefore, this aspect is possibly also a source of motivation.
To answer this particular question of yours, "Is she being creepy?", I'll say, most likely, no, she isn't; she is probably in a group where her behaviour is nothing but more or less usual.
I can't see what could be wrong in comparing the American hug and the French bise, except if by "comparing" you must mean that they represent two behaviours that correspond exactly; that is far from the truth; as to comparing them point by point, why not do that? It's certainly an interesting exercise for a number of research workers versed in questions of civilisation, human behaviour, sociology, anthropology and what not. I'll barely skim the surface and advance one answer easy to arrive at, possibly all that a layman would wish to know. The bise custom is a rather regular thing and every new day asks for one new "bise" (at least for a certain number of days in a row given the context) whereas the american hug is not; it's something that Americans do after fairly long separations for instance or in great occasions, as in times of rejoycing about great achievements, and that they do in times of great sorrow, particularly when it has been overcome. We touch here, I think, upon one of the essential differences. The American hug, if it should be called so, is a much more emotional act. One must understand that the American hug is maybe not any more so strictly American or that it has possibly never been so, as women, mostly, among themselves can be seen hugging themselves in all parts of the world in the same contexts (those just mentioned).
As my comments show, the one armed-hug and the two-armed hug have their equivalent except that the one-armed hug is not a hug but a kiss or two and that the two-armed hug is not a practice found among men, only women are given to it among themselves or with men. It is not usual to use your arms or even only one in an act of giving a "bise" such as the one described in the contexts considered above.