- If you know she's a woman, you should know her name, so use it.
Paragraph 1- Start with the reason for writing- don't start with the background:
I am writing to enquire about studying at...
This paragraph should be short and to the point- no unecessary information.
Para 2- This should contain further information- what does she need to know? I'd say here, that you should say what information you would like.
Para 3- Here you can give your level and reason for studying
Para 4- Closing- what do you want her to do now?
Thanks her and look forward to hearing from here