A few things come to mind.
Take a look a some rain videos and photos to help. Here is a simple drop of water.
http://www.pbase.com/ronnie_14187/image/36165836
As you can see the drop of water is an upside down reflection of the surroundings.
So you could simply render a single frame of the scene (without the rain)
If you have Photoshop or Gizmo.
Open the image, flip it upside down.
If you want you can distort the image with a bubble but it will be so small it is not really needed.
Make a circle selection and remove the outside part of the image. (I recommend after you do this that you scale the image to be 2 times narrower or 2 times taller, water drops to the naked eye look like they are long)
Add some specular highlights and shade on the outer edge if you want.
Save as a PNG so that the layer is not flattened (alpha remains).
Import the image into AS.
Add the Particle "Rain" (Scripts/Particle Effects/Rain)
Remove the vector layers in the folder and move the rain drop image in to the particle folder.
Scale down the drop as needed, duplicate the image layer and vary the size a bit for each one.
Press Play.
You may want to increase the speed and number of particles to get it just right.