Since your major is math, I assume your background is good enough for doing Ph.D. However, a Ph.D. in business is not all about the math. I only focus on your concerns:
1. Working at a hedge fund: please note that research at a hedge fund is very different from academic research. If your job doesn't relate to academic research, it won't add more advantages.
2. Research experience: a lot of people here on Urch will agree with me that recommendation letters and research[academic] experience are the most important. So try to grab some research experience with your Professors, show that you can handle large datasets. That said, you should learn some programming languages, R, STATA, Python, for example.
3. Letters: the world of business academia is small, if you can get letters from Finance professors, it would help a lot. If you can get letters from well-known research finance professors, it would be great. To be honest, letters from math Professors don't help too much in Finance.
Hope it helps.