Since you say that she is new, it would be my guess that she is trying to make friends, tho she obviously is going about it in the wrong way. Seems it should be Bill, and not you, that needs to take action and just tell her outright, that he doesn't appreciate or want her unsolicited advances/attention. If it hurts her feelings - oh well.
And since this is a small office, and everyone seems to know everyone else, I seriously doubt that anyone would believe any rumors or lies she might want to spread about Bill. Afterall, she is the newbie, and anyone that knows Bill, would know that they aren't true - correct?