So after scouring the net for this and getting quite frustrated, I figured it out myself. Short and sweet: In your render panel (the camera) under 'shading', change the 'alpha' dropdown box to 'Transparent'. Et voila. Render with a transparent background (you may need to make sure you have the 'RGBA' button pressed in the 'output' pane on your render panel as well).
EDIT: If you're trying to bake alpha from one mesh to another, you'll need to create a new material on the lowpoly mesh, scroll down and tick the 'Transparency' box, and slide the 'Alpha' down to zero.