I just bought a female umbrella cockatoo from a private owner.

It sounds to me like two things are going on here: First, the 'honeymoon' is over and second, there's some 'new people aggression'. Let me try to address just about everything to do with a biting bird like this (it's going to be 'too much information', but you can use it all over the years).
Parrots love our company, despite how it may seem otherwise. Their biting is quite often actually ‘beaking’, a way that they show of attention, an interaction that's normal for them and would be well received by another bird of their species.
---
In order to teach them that it’s not acceptable for us, when the ‘beaking’ becomes ‘biting’, stop everything. Remove the bird from your presence, be very quiet about it and give them 1 to 5 minutes of silence, no eye contact, no interaction, etc..
---
Then start over again.
---
You have to be consistent with this method. You can tell them "no biting" or "don't bite" in a firm voice (not yelling) with a frowny/unhappy face and eye contact immediately after it happens and as you're about to "shun" them for the 1-5 minutes (any longer than this is ineffective).
*****************************************************
It’s important that the bird knows it is not in ‘flock leader’ position. To help insure this, a modest wing trim should be done. Your bird should not have the ability to get distance or lift out of a flight, just the ability to glide safely to the ground or nearest surface.
When doing this to a previously fully flighted bird there may be some confusion and acting out on the bird’s part, but giving lots of reassurance and consistently being there to pick up and move your companion to where it planned on going, within reason, will help move past the insult more quickly.
When it comes to the cage:
Approach the cage when the bird is calm. Be slow, keep your movements smooth and don’t raise your hands above your own shoulder level – or above the eye level of the bird. Speak with a soft voice and give the bird time to calm down and accept your presence. If it doesn’t adjust relatively quickly, back away until it calms down – the last thing we want is for the bird to injure itself by flailing around in fear.
Remember, patience.
---
Also, respect your bird. Sometimes it won’t feel like stepping up or interacting, just like sometimes you might not feel like doing something. That should be ok. Try again later.
---
Don’t wake a bird up to play and don’t interrupt them while they’re eating.
---
I’ve also found that walking quickly into a different room (which isn’t hard to do with a big macaw chomping down on my arm like a pitbull) will surprise them enough to stop. Suddenly, in new surroundings, I’m their best friend.
---
When the bird bites, it’s getting feedback that it likes and that's why they continue. It might be out of habit, giving them a sense of security in that this action results in that action (or sound) from you. You just have to change the result in order to change the action.
---
When it comes time to take them out of the cage, if you’re really concerned about bites, we’ve used layers of old socks on our arms, hidden by our shirt sleeves so the bird doesn’t get used to seeing the socks. To effect the layers, cut the toe end out of old/clean socks and pull them up over your arm, then pulling your regular sleeve over these layers.
---
Tuck your closed hand down and offer just your arm to the bird with the command (in a normal, but firm voice) to ‘step up’. Put the arm up to the bird’s feet (just above them) at the breast and it should naturally step up onto your arm.
---
If you get bitten (the socks should prevent it from really hurting and reacting), bring the bird to just below your eye level and looking right at them, firmly tell them ‘no biting’, ‘don’t bite’ or ‘be gentle’ (whatever phrase you use should be the one you maintain). Transfer the bird to a day perch, somewhere near you as you watch t.v., work on the computer, read a book, whatever it is you normally do. Make sure there are some chewy toys for this perch and if possible, a food and water bowl. If the bird won’t be out more than a couple hours and you’re sure it ate and drank prior to coming out, it’s probably ok if the food/water bowls aren’t right at this perch (however, a chewy toy is always necessary to keep beak conditioned and relieve stress). Offer a some grapes, berries, pieces of melon or other treats like this that will also provide hydration.
With a new person, have them talk to the bird, look at the bird, interact with it and get close. Offer their arm now and then just as a ‘step up’ exercise, but don’t stress it. When it’s obvious that the bird doesn’t want to do this anymore, don’t push.
---
Eventually the other person will find there’s no biting happening when you reach in to take them out of the cage. It won’t be long before you’re doing this without the ‘socks’. You may still get nipped now and then, but the ‘no biting’ instruction should curb it.
---
Your bird may have decided that you are the 'bird' they like more than the rest of the flock (family and friends) right now. In a few weeks or months - or sometimes years - someone else may be chosen.
---
Until then, dealing with a bitey bird who is also aggressive isn't one of the easiest things to live with.
---
No shoulder riding can be allowed. It wouldn't be unusual for the bird to be looking at someone else and biting whatever is handy and you don't want that to be your cheek or ear.
---
Be consistent. When there’s a bite or lunge - or acting out inappropriately in any way - quietly, swiftly get your bird back to their cage, firmly say "no biting" and then turn your back, walk away. Being abandoned is meaningful discipline for a bird. If left alone in the wild they are susceptible to predators. They really don't want this to happen.
---
Eventually the bird gets the idea that aggression and biting puts them out of the flock
---
Don't keep them away more than about 10 minutes at a time or they'll forget why they’re banished and stop associating it to what they’ve done.
---
If the behavior starts again, you have to repeat the process. It can get pretty tedious, but it'll be well worth it.
---
Encourage socializing by having everyone and anyone else handle your companion. It may take a few layers of socks on the arm (use a couple pair of old, thick socks and cut out the toes so you can pull them on over the forearm; then, to pick the bird up, tuck the hand down and under, offering only the protected forearm)
---
No flinching ! If there’s a bite, have the holder firmly say, "No biting" and give a little earthquake (shaking of the arm). If the behavior continues, reissue the order and have the person walk out of the room, to any other room. This shows the bird that they are not in control, but the human is.
---
The moment your bird stops biting, praise with enthusiasm and feel free to offer a reward. Half a grape, a raisin, piece of apple or small piece of bread with a dab of jelly on it
---
One thing I keep reminding myself is that as much as it may hurt, I’ll heal. The bird, however, may not. They are forever in captivity by us. We can leave the house, find amusements and distractions, hobbies and interests. These birds are completely at our mercy. Their day, indeed, their lives, are only as full and rich as we provide.
If that doesn’t urge our patience and compassion, nothing will.