Heya,
So it depends on whether the white bird has the sky behind it, or foliage (or other darker things). I shoot here in Florida so the sky is always present, and white birds are every where, and it's very easy to under-expose white birds, rather than over-expose. But I take two methods when I'm shooting in these two situations.
Bird in the sky or with sky background:
It's more common to underexpose the bird. Spot metering can help. But if you use evaluative or something broad, it will under-expose the white bird in the sky. For this situation, it's best to use Manual mode and meter and setup your shot. If you don't have that kind of time, or simply won't do it, using a semi-auto mode (AV) you can tighten it up by using spot meter or partial meter, and adding in some EC (I would go with +2/3 to +1, but it depends on the camera model and what you want out of it). RAW is very important here, because you'll rarely get perfect exposure on a white bird in the sky. So being able to get near proper exposure or slight over-exposure would be ideal, rather than under-exposure. RAW lets you make up that difference with more ease and cleaner.
Bird against foliage or darker backgrounds:
A lot easier to expose properly, but it's easy to over-expose the bird in this case depending on what meter you use, like evaluative. It's still best to use Manual and meter and setup your shot yourself. But if you're using AV or something, again, it's best to use some EC, and depending on what meter you use.
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I generally shoot AV like 90% of the time, due to fast changing light conditions (clouds; brush, etc). I generally always shoot with my EC at +1, if not even +1 & 1/3rd and I'm using partial metering. I don't use spot really unless it's critical. I do not use evaluative, because I'm always shooting animals in habitat and here in Florida that's often including a bright sky or reflective water, etc. Evaluative just under-exposes most everything in my experience when you have big bright elements in your composition and that dark brown bird is going to be under-exposed. I try to base my exposure on the subject, not the environment, so I tighten my metering (but not so tight as to use spot, and this is why I like partial). I shoot RAW 100%, because my exposure is rarely perfect, so RAW let's me have another stop or two of correction in post to get it right or at least get it to look how I wanted.
These are all AV and Partial Metering with +1 EC, shot in RAW. My common way to deal with white birds, is to alter exposure in RAW by a little bit to get the white to how I want it, then I drop highlights by a little bit to keep the white from glowing. If I have to drop exposure and lift shadows to make up for it, so be it.

IMAGE LINK: https://flic.kr/p/CfG6Wc
IMG_0063
by
Martin Wise
, on Flickr
IMAGE LINK: https://flic.kr/p/C8pF5t
IMG_0050
by
Martin Wise
, on Flickr
IMAGE LINK: https://flic.kr/p/BNwEf1
LE1M4407
by
Martin Wise
, on Flickr
Back lighting from sun on white bird:
IMAGE LINK: https://flic.kr/p/AMrbAS
IMG_9762
by
Martin Wise
, on Flickr
Very best,