Ask for a sit-down meeting with your supervisor, outline your current positive job experience, let her/him know what your goals are, and ask why you've not been given more opportunity to do additional work. I'm assuming your job performance feedback has been positive so far, and it may be that there's no time/training ability to bring you up to speed on other duties. Hopefully, you'll get a straight answer, and it will be one that you can accept. Your supervisor's avoidance is one of two things....they're too busy to train you to do more (and they're comfortable with your job duties as they stand), or they don't feel you're ready for more responsibility. I suspect it's the first one. Figure out how you can dive in and help out without your supervisor having to set everything up for you. If she's overworked (and I know the feeling), she's not going to have time to sit down and supervise as you learn the new ropes. Instead, maybe you could grab some charts, do some audits, present your results, and then say, "hey, look what I did....". Or ask the person who does the other jobs you're interested in if they'd be able to cross-train you for when they're out of the office. It may be that these other employees are unwilling to give up their work, and the supervisor doesn't want to make waves......lots of politics in every office that we might not know about, but you have the inside scoop and should be able to figure it out.
There's nothing I like better in my office than a self-starter. Maybe you need to just take the initiative.
Please don't think that you're not 'doing anything of importance'. All jobs within the revenue cycle are important, and you wouldn't want this attitude to leak out to your current manager. (or maybe she's already sensed it?) My most recent CPC-A hire started out doing data entry as a part time employee. She hung in there for two years.....because my hands were tied in terms of being able to bring her on full-time. Yesterday, I was able to do that. So sometimes it takes awhile. This is healthcare...not Hollywood.
Hopefully, I've given you food for thought. Good luck, and please let us know how it works out.