But it's my job to grab things and do stuff, like measure ear length or weigh them. Lots of things depending on the project I am on. So yes, I get bitten. And this has become a point of question again since I posted in a side note that scarlet tanagers bite, but that it doesn't hurt much.
Different species tend to either bite a lot, or not. Some birds never seem to realize that might even be a thing, while others, most notably the chickadee, do nothing but try and bite. Some can give a pretty good pinch, especially the ones with a strong bill like a grosbeak, but mostly it really isn't hard enough to do much.
And, one of the times I am most likely to get bitten is when taking the photos to document the species capture. See, when taking animal measurements I can control the whole animal including the mouth, but for the photos the head needs to be fully in the clear. Which of course allows it more freedom to take a nip. So while I normally just ignore the photos that don't well-document the species for our records, I do have other ones that show what the animal was doing while I was trying to get a good pic.
And to satisfy curiosity, here is what a bite from a scarlet tanager looks like. See, not much, but if it gets you in the soft spot between your fingers you'll know about it.