Store the "radii''s" ie, the length from the center of the object to the left/right edge and from the center of the object to the top/bottom. Each frame you test the two objects radii''s against eachother, if BOTH the x and the y radii''s overlap, there is a colission. This is only for bounding boxes though but that seems to be what you want? You will get pixel-perfect colissions with this unless the speed is so great the ball will "move through" the bat.
This also eliminates this error:
|-------| | | |----------------| | | | | | | | | | | | | |----------------| | | |-------|
Ok these objects got no vertices inside eachother, some systems would not recognize a colission in this.