Girls are more horrible then mens in general?

In your case, it doesn't sound this girl was that smart and you got the better of her but for some people, using bitchiness, side remarks, putting people down and insulting them, all done in an implicit way, that almost appears "friendly/humourous", this is all just second nature.

Whereas for me and I'm sure a lot of less socially-skilled, more straight/honest people, it takes a conscious effort to hurt/insult people.

I've always been mesmerised by these people who can put people down in a social environment to impose themselves, to make people look bad and make themselves look good. I wonder how their brains work. It's almost as if they don't even need to think about it much. If I ever make any joking comment, I'm always too aware of whether I might hurt/insult the person I'm talking to.

Just to give an example of a typical conversation at work with a bitchy person:
Manager: "So did you check the orders for last week?"
Bitchy person: "Yep we've gone through the list and verified the quantities"
Average Joe: "Actually I did notice something a bit strange with Monday's figures. I'll check that"
Bitchy person: "Oh don't worry about that. I've already looked at that. You were probably half asleep when you got to work" (with a nice big fake smile)

I probably haven't even written a very good convo there and the bitchiness is probably too obvious... But the subtle bitchiness there is something that I've never understood. For one, I've never felt the need to do so and the other thing is that I don't even know why I would want to go out my way to make someone look bad like that.
Maybe I'm just socially inept because it seems that there are more people skilled at this stuff than not.

Yes this confident/fun side of some bitchy people does attract other people, despite the bitchiness. But I'm also talking about the fact that some people will hang out with others, even if they don't like them because of "fear" i.e. they stick with them because they feel that their social status will be more secure that way, even if they have no true affinity with the person.

A simple example would be a bitchy person putting down a good friend of yours right in front of you. Someone with no real morals and who is more worried about their reputation/image/popularity, might not even say anything, in case they get on the wrong side of this person.

Of course a certain amount of confidence is required to behave like a bitchy person, but quite often, it's to hide a bit of an inferiority complex. I know a few people who really could be picked on big time because of the way they look, their lifestyle, their job, but they never do get picked on because they're always one step ahead in case someone comes round to insult them. They've turned "putting other people down" into such a skill that despite all their flaws and shortcomings, most people will not pick a bone with them. These people will also stick to social surroundings where there's no risk of that happening.

Well there's certain levels of putting down. There's just the joking, ladish humour between mates which is totally harmless because each of you know that you won't take it badly.

There's the straightforward insults but then, there's all that space in between where insults can be disguised as jokes or ambiguous sentences. Bitchy people play in that space. They usually try to make sure they don't go so far that it's obvious that they're aiming to insult/offend the other person.

To be totally honest, I have some good friends and then I have some not-so-good friends who can be fine in certain groups but in other surroundings, will put other people down (me included) because they just enjoy putting people down and making themselves look good that way.

I've just never been that tactical in my socialising. I've always believed in being a good mate who's there when you need him, who'll stick up for you, rather than trying to make myself look good at the expense of others. I simply don't believe in putting people down completely just to look better, even if that might be a solution to get more respect. I'd say that the majority of people I know do it to a certain extent, either consciously or not. I will never go further than making a joke when I know that the person won't take it badly and it will usually be an isolated comment rather than a whole tirade.

This whole bitchy stuff isn't really about people liking you or not liking you. I know bitchy people who actually like the people they insult but the only way they know to get by in a social environment is to put down those who seem like easy targets.