So did she pay? When she said she was super busy -- I hope you told her that you needed to collect her remaining balance before she leaves town. Do you accept credit cards? If so -- get the cc info from her over the phone and run her credit card.
I know it's nice to get the big dollar customers...but from personal experience (see my thread on difficult customers)...sometimes they just aren't worth it. Unfortunately some of these wealthy people seem to think they are entitled to pay what they want, when they want, IF they want.