Recommendation Letter v.s. Ph.D. opportunity
It is extremely common in my experience to ask a professor for a letter of recommendation while at the same time expressing interest in pursuing further work with that same said professor. I did it myself.
Professors realize that they might not be your only option. Placing their students in graduate programs (where ever they may be) always reflects positively on them.
You have actually done much of the hard work already. You have already talked with this professor about your future plans and sought to gauge her opinion on your becoming her student. If she seemed at all open to taking you on as a student, she will also be open to writing you a letter of recommendation.
I would say something like the following:

Hi Professor McGonagall,
You and I spoke briefly last year about some of my plans for graduate school. I am applying to several programs and I am in hopes that I could obtain a letter of recommendation from you. As one of my options, I am planning on applying to the program at [your university], with you as my potential advisor. Is there a time we could meet to discuss these items further? I am available any time next week on Wednesday or Thursday.
Thank you,
mathvc_

Any reasonable professor would be happy to discuss bringing you on as a graduate student and writing you a letter of recommendation for other options as well. My master's advisor did so for me; I have also done so for my own students. If this professor tells you that she will only write you a letter for her own program and is offended that you would look at other options, you do not want her as your advisor. It would be very worrisome to me if advisor was only willing to take me on as a student if I applied to no other programs. It signals an advisor who is a controlling advisor.