Her mother wished her to learn music; and Catherine was sure she should like it, for she was very fond of tinkling the keys of the old forlorn spinner; so, at eight years old she began. She learnt a year, and could not bear it; and Mrs. Morland, who did not insist on her daughters being accomplished in spite of incapacity or distaste, allowed her to leave off. The day which dismissed the music–master was one of the happiest of Catherine’s life. Northanger Abbey, Chapter 1

The Morland family were not poor,and could afford to purchase the expertise of a master.The Bennet girls, though at the fringes of gentility probably did have access to masters, though not a governess.

As Elizabeth Bennet’s tells Lady Catherine;

… but such of us as wished to learn never wanted the means. We were always encouraged to read, and had all the masters that were necessary. Those who chose to be idle, certainly might.” (chapter 29).

In this same chapter Elizabeth assures Lady Catherine that contrary to her assumption,their mother did not bother herself much with their formal education;

“No governess! How was that possible? Five daughters brought up at home without a governess! I never heard of such a thing. Your mother must have been quite a slave to your education.

Elizabeth could hardly help smiling, as she assured her that had not been the case.”

Meryton was not so small a town remember – it did after all, possess a Mayor. It could have provided masters for dancing, as it did boast of having an Assembly Room, and someone had to be able to teach the most fashionable dances to those wishing to attend. It also might well have been able to provide music and drawing masters.

But you are correct in assuming that locality was all important.If one lived in a remote district then obtaining the services of msters would have been difficult and expensive .May I suggest you read The Gentleman’s Daughter by Amanda Vickery for views of life in remote Northern England during the 18th century.

As to gentility, being a tutor or governess was a respectable trade. Indeed it was the only route for work open to many impoverished single women. Look at Miss Taylor, Emma’s governess, who was undoubtedly genteel, and eventually married rather successfully into the lower reaches of Highbury society. As for men, Fanny Burney’s father Charles was a musician who also acted a music master to aristocratic circles, particularly while he lived in Kings Lynn, Norfolk (where Fanny was born) and her uncle Richard was a dancing master in London.

Another book you might find helpful is A Governess in the Age of Jane Austen by Joanna Martin.This book is based on the journals and letters of Agnes Porter who was a governess to aristocratic families during this period,and it gives a very good insight into the type of life such a governess might well expect.