Surprise her. Start the message of strange, don't ask questions, try to avoid worn-out cliches that are very easy to slip when writing. Think of a creative compliment, a suitable only for her to show that I appreciate her personality. Surprise her with a community of your interests or your sense of humor.
Be a gentleman. Of course, after centuries, manners have undergone very significant changes and, perhaps, you should not start a letter with "Greetings to You, gracious Madam!", but to show a good education is desirable. Even in the correspondence in social networks, when the priority is getting the speed of message delivery, there is no need to neglect such simple words as "thank you" and "please."
Don't be Intrusive. Of course, should show interest in the person to whom you write, but to write her every ten minutes if you don't receive a response - not the best option. Be prepared to answer her messages promptly. But when your three letters were left without response, think twice before writing the fourth.