It strikes me that this is a bit more nuanced than the girlfriend being unreasonable.
What occurs to me in your situation is that your fiancé has suffered a traumatic event, as a result of which she's now reacting irrationally. The bird hates me, it's vicious, it'll happen again etc. We know it was an accident, that there are lessons to be learned and that it should really be chalked up to experience, but convincing her is going to be hard work. She's had a horrible experience, it's not her pet or her responsibility, and she deserves a little sympathy here.
I actually think you've done the right thing boarding the bird at this point - you obviously need to work things through with your fiancé and the tension you'e describing is not going to help the bird settle and behave calmly. I had a situation with a friend who regularly stays over, and who received a nasty bite from Alice within a few minutes of meeting her. For a while my friend was obviously on edge when Alice was near her, and Alice's response was to go into defense mode and take swipes when my friend came within reach. More experienced voices than mine might chime in on this but my suspicion is that birds don't recognize fear as such in humans: they process it as negative energy and view the fearful person as a potential threat. Tension building between your fiancé and the bird is only going to make things worse.
I think now things are calming down and while the bird is out of the house, it's time for a council of war with your fiancé and a look at your options. Explaining how important the bird is to you and how it is a lifelong commitment to take on an animal such is this is crucial; I also think it's important that she knows you take some responsibility for what happened, that perhaps you could have educated her better about the nature of birds as companions and the reality that the more you interact with a bird the greater the chances of a painful bite. Then it's a question of what options she's willing to consider: the suggestion of a behavioural specialist is an excellent one if she's prepared to give it a go: that way apart from a clear indication of your commitment to resolving the problem you get to improve your own handling ability of the bird, deal with issues such as screaming, and your fiancé will develop a far better understanding of how the bird's mind works as well as the confidence that she can coexist with it.
I wish you the best with it: the thought of choosing between a partner and your bird is a heartbreaking one, and I hope it won't come to it.