Hello, and welcome to the Parrot Forums family!
I've always felt that the whole "my bird hates men/women" thing tends to be a misunderstanding of whatever is actually triggering the biting behavior in the bird. Now, is it possible that a person of a particular gender might strongly resemble another person of that same particular gender who in the past earned that bird's ire? Sure. But it wouldn't be a general man vs woman thing. Know what I mean?
But on to your questions. First thing to do is begin paying strong attention to your bird's body language. What many people don't realize is the extent to which birds communicate via body language. Much of what they "say" to one another... and to us... goes unnoticed simply because we often don't recognize what they are doing as communication. So in many cases, by the time the bird bites you she has likely already warned you several times over and is now acting out of exasperation. (Of course, a bird might also be quick to bite after having been unintentionally taught in her prior home that it's the only form of communication that we humans listen to. This, however, is related to the body language thing as it is the natural result when said bird's other warnings have been continually ignored.)
Now, while we will never get to the point that we can comprehend
everything they are trying to tell us, we can at least achieve a rudimentary understanding of their more basic communications. And this will help immensely with the biting situation, as you will be better prepared to avoid the bites in the first place if you can get a feel for when they are coming. (Here is a link to a great thread that focuses in-depth on body language and bite-avoidance:
http://www.parrotforums.com/training/57935-brainstorming-biting-parrots.html)
Btw, as if learning to read their body language wasn't difficult enough, some of the indicators that you need to look out for turn out to be individual to one particular parrot. For instance, my male eclectus, Jolly, gently takes my finger in his beak. Depending on the context, he's either being affectionate or stopping my hand from doing something that he's not really thrilled about. The difference is subtle, but you soon get a sense of which is which. But Maya (my female eclectus), on the other hand, is a bird of an entirely different color (both literally and figuratively). When she gently beaks me, she is actually communicating to me the beginning of a countdown. There is something that she wants - urgently - and she's letting me know in no uncertain terms. (This sometimes occurs when she's on my hand and waiting as I get her food bowl together.) Each successive beaking after the first gradually increases the pressure applied. Now, I have no idea what happens after the fourth... as I've never taken long enough to reach #5 (my momma didn't raise no fool!), but given the mathematical precision with which each squeeze increases, I'm fairly certain that the 5th would be rather uncomfortable and the 6th would likely be ouch-worthy. But I understand her communication for what it is and act accordingly.
And understanding leads to the second step, which is determining the trigger. It's all well and good that we come to recognize their body language, but what can we do with that knowledge? Well, with a lot of observation and deductive reasoning, we can figure out what exactly is leading to the reactions to which we have become attuned.
Let's look at your example. (I love, btw, that you say "...for no
apparent reason" when you mention her biting you. Apparent is the key.) Once you recognize the body language indicators to look for, you can consider the circumstances around you when you see it happening. For example, let's say your new ekkie has already formed an attachment to your husband. The trigger might have been something as simple as your husband walking into the room. Why? Because the instant he (her favorite in this presumed scenario) walks into the room, you become an obstacle to her being with him. The initial nip, and then the harder bite, were her attempts to get through to you that she wanted to be
over there, with
him.
Or, if you were her favorite, it might have been a warning bite. "Look out! That suspicious looking guy is back!" Or displacement biting.
Even something as subtle as a lighting change that shifted a shadow on the wall and scared her silly could've been the culprit. Or she might even get bored easily and was trying to get you to engage her instead of just chilling together. You won't really have a definitive answer until you've taken the time to observe.
Of course, the very short length of time you've had her also factors in, but I focused on other aspects since she walked over to you and climbed your leg. So shyness doesn't seem to be the issue.
Whatever the cause, identifying it is job one. Then adjust your behavior appropriately. If it's something that can be avoided, make what changes you need to make that happen. And if not, you work further on bite-pressure training. (Remember the example I gave with Maya? Her countdown was something she developed once I taught her that just up and biting me was not acceptable.) Here is a thread on bite-pressure training you'll definitely want to check out:
http://www.parrotforums.com/training/63988-bite-pressure-training.html
Another thing that helps in the meantime as you are learning her body language is to carry something palm-sized in your hand, like a bird-safe piece of wood or plastic, that you can use as a "distractor". This is good in that it gives them a substitute for your flesh when the urge to eat you comes along. Just interpose it between you and the offending beak if she goes to strike.
As for the a safer way to carry her around until she stops biting, you should get a T-perch. Shaped just how the name implies, it allows you to hold the shaft and give your bird a non-flesh perch to step up on that she can't easily traverse to get to your hand. There are quite a few members here who have their birds stick-trained for that very reason... or for birds that get a bit... unpleasant... during their hormonal seasons.
Hope this helps, and don't hesitate to reach out if you have more questions.