I think you'll understand the sentence if you think of it this way: the word "of" does not go with "entertain," but rather with "opinion." You can "have an opinion of someone," or "hold an opinion of someone," or "entertain an opinion of someone." In general, when you're talking about people, the preposition that follows "opinion" is "of." To "entertain an opinion" is a somewhat literary usage; we can also say that someone "entertains" doubts, illusions, questions, ideas, etc.

To entertain in this context simply means “to hold of”. Bessie and Ms Abbot just held a bad opinion of the speaker. “..to entertain of me” is just is a fancy way of saying the same thing. You have to keep in mind that this is highly elevated literary speech and no one really is likely to speak this way. To entertain an opinion of someone is to hold an opinion of someone. That’s all.

It means the opinion they hold about me. The speech in this book is old as it's an old book. It's beautiful English but nowadays people don't speak like that in general English.

1st off your English must be really good if you are reading a book from the 1800s and secondly, no English speaker would say that honestly. I am 99.9% sure you will never run across this in spoken English or even modern books. Anyways, I believe the "entertain of me" part is referring to how the two characters B and Miss A think of Jane. If they thought of Jane as bad, then in this scenario where she was resisting" all the way" reinforces the way B and Miss A thought about Jane. So they have been, in a sense, "entertaining" a certain idea of who Jane is and now Jane's actions have reinforced it. Replace the word entertain in this sentence with... Think about me or something like that. Hopefully that makes sense....hard to explain this one.

I used to be muddled about this too. Usually, when we say "entertain", we think about music concerts or magic shows. However, the word is used in the sense that you invite someone to your home and serve them drinks. Another meaning is that you think about something, hold something in your mind or be willing to consider or accept something "The General refused to entertain the possibility of defeat." (the example sentence is from the Cambridge dictionary) In my opinion, this third meaning is the option that you're looking for. I hope this was helpful for you.