Thanks!

Definitely follow up, esp if she seemed enthusiastic. But yes, keep it to just once. If you can, try to find out if she's in the office or something. You don't want to "waste" your follow-up by sending it in the middle of her vacation.

You can follow up once. Any more than that it becomes annoying.

I reached out to a former supervisor about an opening in her group and she seemed enthusiastic about having me rejoin the group. She told me to send in my resume to HR and now its been about a week, I haven't heard anything. Should I follow up or is that annoying?