Yes. You can get management experience working in ANY field.
Think about it – whatever job you have, you have a manager, right? How do you think that person got the job? By first having your job and being promoted.
So, get a regular old job, preferably at a business that’s growing fast, and work hard at it. Don’t goof off like the other employees. Act responsible and help the more junior/newer employees when they don’t know how to do something. This will mark you apart from your co-workers as someone who can handle the responsibilities of management, and you’ll probably soon be trained into an assistant manager position, and from there, you’ll be gaining management experience.

self employment or working at a fast food restaurant as a manager trainee—both will supplement your admin experience.

Try an Internship as a manager

Not possible without practically working. You might have read so many books on management but until and unless you are exposed to real problems of the management, you won’t be able to get any experience.
Your 6 years’ experience in administration may however make your management studies very easy for you. You will be able to make comparison of the theoretical knowledge of the books during the your studies with what you gained from your paractical experience. Your BS in Business Management will definitely refine your knowledge of management/administration.