It is possible to balance tact with a direct approach. Be very clear as to your expectations but measure your approach with an understanding of today's economy. You could explain that you have had problems with clients' returned checks and to avoid the extra fees that will have to be imposed from the bank for your client, you've decided to accept cash as your prefered form of payment. No doubt, she'll realize she is among those clients, and it preserves her dignity as well as leaving an open door for future business from her.
I've got to say that I like Kathleen's comment. Strong, direct, and still communicating that you want to continue a business relationship with the customer. My only additional recommendation would be to go over it in your head a number of times or possibly role-play it with a friend. Get used to the words coming out firmly but with a smile. I hope it goes well. Let us know how it works out, I'm curious. Keep up the good work.