'She lifted a doughnut and took an immense bite'
One guess: if she 'took an immense bite' of something, she totally immersed herself into the taste of the dish. if she 'took an immense bite', no other taste or flavor could exist.
More fruitful: she made an immense bite
What does seem more natural to you?
Are your two guesses the meanings of the sentence? If so, you're making much more of an "immense bite" than you need to.
She lifted (or picked up) the doughnut and took an immense (or large) bite. I’m laughing as I say this, but gluttony may be a better explanation than immersion in the taste of the donut. She likes donuts and can’t eat it fast enough. I suspect that she does the same with cakes and cookies. Ahh! . . . and chocolate pie, as well.