How should I understand this sentence in the movie Bridgerton?
It's not standard. It seems to me a muddle of the following:
- not one bite (i.e. no bites at all)
- but one bite (i.e. only one bite)
The latter usage is sense 1 of the adverb "but".
The old lady's sentence, with "but not one bite", is not grammatical, but then the scriptwriter might well have deliberately made the character say that, to show a peculiarity of that character's speech.