Screen-space is basically a 2D entity, so instead of a bounding box think of a bounding rectangle.
Here is a simple way to compute it:
- Project 8 corner points of your world-space bounding box onto the screen using your ModelViewProjection matrix
- Find a bounding rectangle of these points (which is just min/max X and Y coordinates of the points)
A more sophisticated way can be used to compute a screen-space bounding rect for a point light source. We calculate four planes that pass through the camera position and are tangent to the light’s sphere of illumination (the light radius). Intersections of each tangent plane with the image plane gives us 4 lines on the image plane. This lines define the resulting bounding rectangle.
Refer to this article for math details: http://www.altdevblogaday.com/2012/03/01/getting-the-projected-extent-of-a-sphere-to-the-near-plane/