No doctorate, undergrad degree. I have experience teaching college credit courses to advanced high school students, summer programs. I don't assume that to mean much.
When I went to school the faculty was comprised almost entirely of individuals who were esteemed professionals in their field. In four years I don't think I had one instructor who held a doctorate, or a bachelors degree in some cases--and that school is considered to be one of the world's finest jazz performance programs (heh, jazz).
What you might not realize is that, while it is indeed common in music schools for many of the faculty to be practitioners who do not have doctorates, it's also common for many of those positions to be contract positions. The faculty with whom you dealt might well have been around for a long time, but that doesn't mean they held tenured or tenurable professorships.
In the school of music at my own university, there are about 30 tenure-track faculty, the vast majority of whom have PhDs. All the composition faculty have PhDs or DMAs, and there are no contract faculty in that division. There are over 50 contract faculty, most of them instrument, voice, and ensemble instructors; about a quarter of them have PhDs or DMAs too, and the others have Masters-level qualifications.
Conservatories and other free-standing schools might behave differently, but it does sound to me like you need to learn a bit more about how music works in universities. Are you still in contact with some of your old teachers? They might be able to give you a more realistic picture of what you could expect on the job market.
Technically speaking, with only an undergrad degree you are probably not qualified for any of the listed ranks--not even at the clinical level. Your professional qualifications
might be considered to compensate for the lack of a graduate degree, but that would depend upon the courses they need this person to cover, and the accreditation issues involved.
Is there no list of required qualifications for this position?