Generally if someone comes up behind me I slow down and move to the right so they can pull along side. (I live in a small town so 9 times out of 10 it's someone I know--ha!). After a few minutes of chatting the ride seems to sort itself out into one of several scenarios:
1. We decide we want an easy ride and nice conversation so we ride side by side and talk (the most common).
2. The other rider wants a harder ride and waves and rides off.
3. *I* want a harder ride OR the other rider is annoying me OR I just want to be alone. In this case I will often change direction (take a turn off or alternate route). It's easier than saying "go away". :p
4. Very rarely, the other rider will be a training partner and we'll decide to work together and take turns pulling each other.
Another trick to get rid of an unwanted drafter is to stop. Just pull over the side and make an adjustment to your bike.
And yes, you should always always announce yourself when coming up behind anyone (cyclist, jogger, dog walker) on your bike. It's just plain rude to startle people. A simple "hello" works pretty well for me.
So, what would I have done in your position Cyclingnewbie? I would have slowed and pulled to the right. She would have either slowed and aknowledged me or (more likely given your description of her behavior) ridden past me. I would let her gap me, then resume my own pace. I would let her know by my actions that "racing" on a bike path (is this multi-use? with walkers and joggers and kids-on-bikes?) is silly, rude and potentially dangerous.
