What does "she does go on a bit..." mean in the context?
As often as not, we then immediately start grumbling about the very people from whom, a moment earlier, we could apparently hardly bear to tear ourselves. ‘God, I thought they were never going to go!’ ‘The Joneses are very nice and all that, but she does go on a bit . . .’ Even when we have thoroughly enjoyed the gathering, our appreciative comments following the long goodbye will be mixed with moans about how late it is, how tired we are, how much in need of a cup of tea/strong drink – and how nice it is to have the place to ourselves again (or to be going home to our own bed).

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It means that she talks too much - for too long.

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It's an expression which means that the person talks a lot, perhaps repeating themselves, being long-winded etc.

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Perhaps it is worth adding that the phrase "a bit" is polite understatement. First the speaker says "she does go on," meaning "she talks too much," but then softens it by saying "a bit." "I don't really like to say bad things about people but she talks too much."

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I try to write useful answers on italki, but I do go on a bit.