(image from amazon.com)The Beekeeper's Apprentice by Laurie R. King
I mentioned this on my last choice, and since the last one I chose was a bit boring, I've decided to go with one I've read. Since it's based off Sherlock Holmes it still fits with your expectations that I'll choose a classic ;)
Here's the description Amazon used from the School Library Journal:
At 15, Mary Russell is tall and gangling, bespectacled and bookish. In 1915, the orphaned heiress is living in her ancestral home with an embittered aunt she has plucked from genteel poverty to act as a guardian until she reaches her majority. In order to escape the woman's generally malevolent disposition, she wanders the Downs. On one such outing, she trips over a gaunt, elderly man sitting on the ground, "watching bees." This gentleman turns out to be Sherlock Holmes, and the resulting acquaintance evolves into a mentoring experience for the young woman. The story is well written in a style slightly reminiscent of Conan Doyle's, but is also very much King's own. The plot is somewhat predictable, but the characterizations are excellent and the times and places are skillfully evoked.
I will say that you don't really identify with her, and the feminist/erudite undertone is a little over the top, but it's an entertaining mystery.


