I would generally not use the term 'bump map' to describe it as that's a reference to an entirely different, very specific technique that just so happens to use a similar-looking texture as an input.
In simpler terms, you're using a distortion shader that adds or subtracts a value to the texture coordinate (distinct from the value sampled from a texture at that texture coordinate, though the actual offset would be taken from a second texture) depending on the location onscreen. tonemgub's soltution is basically to paint a texture that contains offsets gradually pointing towards the middle of the screen, with decreasing magnitude as you move away from one of the corners. It would work, but is likely more computationally expensive than it could be.
Fortunately, folks have already worked out how to do most of this with math. If you're interested in a really detailed CRT monitor simulation, give this neat site/shader a gander.