How to ask your boss about a position that is open above you?

I currently work as a Help Desk technician, and there is a position that is open as a System Administrator in my company. The job requirements say 2 years work experience or equivalent degree. I have the work experience, however I still feel like I do not have quite the knowledge needed because I have no formal classes, nor a degree. I know some of what the System Administrators do, but I am still a little hesitant because some of the phone and networking things I do not know about. I have a good working/learning relationship with the 3 admins that we currently have, and usually have to discuss things related to work with all of them at some point almost everyday. I would like to apply for the position, which is still under my same boss, however my boss has not formally offered me the position. However she did mention on a recent busines trip that I could still do online classes and be a System Administrator (due to being on call 24/7 every 4th week). I have a feeling that she would likely hire me due to some of the discussions we have had, and the scope of most of my work has changed from Help Desk and support related to IT project and advanced troubleshooting. She may have been hesitant to offer me the formal position because I do throughly enjoy what I am doing, and I am still in school. The position has been open for nearly 2 months and my boss hasn’t done any interviews, and I havent seen a stack of applications piled up on her desk (not that Im looking through her stuff, but she usually lets things like that stack up and then go through them all at once)

I am wondering of the best way to inquire about the possibility of applying for the position, or if I should just go ahead and send in my application. If so, do I need to include a resume, etc.? I am unfamiliar with internal applications, and am definitely wanting to learn, even if it is recommended that I not apply for it.