How long ago did you ask?
What was her reason for turning you down?
Has she given you any signs or hints she may be interested?
Asking her again would be OK as long as there was no tension when you asked her last time. If she acted funny, or avoided you for any period of time it is better to not ask her out.
The excuse she gave could be a logical one so this is nothing to prevent you from asking again. Since she is a very busy lady I would suggest asking her on a informal date, such as lunch or to grab a quick bite for dinner. This helps take some of the pressure off when thinking about getting involved with someone. It sounds like she is very active and with all the responsibility's she has a relationship can be difficult to maintain. The key is to give her the idea that getting together with you is not a commitment but just a chance to get out of the house and have a little fun.