“Surreptitiously” is better. It’s generally the right word to describe an attempt an action that a person is trying to do without being noticed. Another example: “He surreptitiously put the note into her purse.” “Secretively” is a better choice if you intend to focus on keeping other people rom learning INFORMATION you don’t want them do know.

One of the nice things about English is that you can also say it this way, and it works just as well, if not better: "Mary slipped surreptitiously from the room."

Quietly