I am a first year PhD student in France, born and raised in India. It is not customary in here where I am doing my PhD to call one's adviser boss but I do, partly due to my reluctance to call her by the first name, partly attributed to the culture in which I am brought up. As one comment suggested, "Dear professor" would have been an appropriate choice but she doesn't have any teaching duties and is a full time researcher. I would have used "Dear Madam" if I were in India but no one here use that. I think "Dear Dr. X" is too formal and no one here use that either. Many prefer "Hi X" but I think that is too informal. Now that I am writing an email, Is Dear Boss an appropriate salutation? If not, what would be an appropriate salutation in a formal email?
"Dear Professor X" is still probably still appropriate. Even if they are a full-time researcher and aren't teaching, their official position is probably some variant of "Professor." If their job title is not professor, then I would just go with "Dear Dr. X" and accept that it might be a little too formal.
At least in the US, I would pretty much never use "Dear Boss," even in an email sent to my actual boss in industry. It sounds awkward and weirdly removed. If you want something more formal than a first name, stick to "Ms./Mr./Dr. X."