Congratulations on your BSN! It should open more career doors for you.
Of course, you should go ahead and start looking & apply whenever you meet the (new) job qualifications. But in the meantime, I encourage your to take advantage of any 'leadership' opportunities in your current job. Volunteer to serve on task forces, committees & special projects. These will provide you with experience in leading teams. These 'added' responsibilities will show a potential employer that you have leadership ability and experience even if you haven't actually held a management job yet.
Wishing you major job MOJO!!! Go get 'em!