I suppose if there is one thing I have learned with birds is to always be "chill." For example, if I do need to go inside to get the cam, I just casually move about as if I don't have a care in the world and I don't even know the bird is there. Not sure if that helps keep the bird calm, but it does help me
In this case I was actually able to progressively move closer to the bird several times before it took off. I always start at the door, just to get something, then I slowly move forward a bit - not looking at the bird - then stop, grab a few frames, then try again. This time I was able to get quite close.