Hi!
Glad you asked!
First it must be made clear that a Bachelor of Music Education degree (BMuEd) is different than a performance, Bachelor or Music degree (BM). The BMuEd requires that you learn about many instruments, and conducting, so that you are able to teach in public schools, where a more general education is required. A BM degree certifies that you are a performer ready for the professional world of performance. It usually is necessary to go onward and get an MM degree in order to be competitive in this VERY competitive performance world. A Masters in Music Education is required to teach at the high school level in some States and allows for much better salary. An MM is required (minimum) to teach at a university in studio, master class, and chamber music coaching. SO: If you are interested in performing primarily with studio teaching at an institution, go for a BM then MM (then perhaps DMA). If you wish to teach in public schools, a BMuEd is your program.
Now, whether you can obtain the necessary skills and musicality to enter a program at university level in either degree path, is entirely up to your dedication and natural abilities ... and, I might add, the equipment that works well with and for you. Your private teacher is likely a good judge of all that. If you have no private teacher, I would venture that your chances are much reduced... though not impossible.
I require that an entering Freshman be able to play all major and minor scales in a variety of bowed patterns, and pizzicato, in at least two octaves; a Baroque Sonata of some sort, and have some orchestral repertory or strong jazz repertory background. See my web site at the University of Arizona for more information:
www.u.arizona.edu/~neher and look for the syllabus descriptions.
Best to you!!
PN
requirements for college 
