It’s a matter of degrees of formality. ‘Should you admit her . . .’, . ‘Were you to admit her . . .’ and ‘If you were to admit her . . . .’ are all particularly formal. The informal, and more usual, construction would be ‘If you admitted her . . .’
The sentence is basically an instance of what is sometimes taught to foreign learners of English as the Second Conditional. The differences in style can perhaps be better appreciated by stepping away from this example from nineteenth century fiction, and looking at a sentence that might occur in contemporary English. Suppose that I have a friend who wants to catch a train. I know that he could if he hurried, but I also know that he won’t, because he’s unfit. In those circumstances, I would normally say
If you ran, you’d catch the train.
The three formal versions, equivalent to Charlotte Brontë’s sentence and the two
alternatives I have proposed, are:
Should you run you’d catch the train.
Were you to run, you’d catch the train.
If you were to run, you’d catch the train.
You will see that the degree of formality shown in these constructions would be quite inappropriate in the situation.