Last year, I started collaborating with a high-level professor in the field in a good but not the best institute. Before leaving there, I discussed with her a possible opportunity to having her recommendation letter. Also, I asked about the possible opportunity to becoming her Ph.D. student. She seemed okay about this, however, she told me there will be an interview.
Now, I want to send an email to her letting her know that I want to be considered as her potential graduate student while having her recommendation letter because I do not know yet what options I will have. Her recommendation letter will really help me, but I do not want to lose the chance to be considered as her potential graduate student.
I worry that my asking her for a letter of recommendation, while at the same time asking to be considered for admission as her own graduate student, might look like I am too ambitious! How does it sound to a professor? What are the possible reaction of a natural professor to this? Is it mature and rational to send such an email? If I were the professor, I will definitely realize the student is looking for as many opportunities as feasible, however, I may not consider him as a potential student. Please help me to clarify my thoughts on this point.