I've got a bit of damage in the corner of my car's bumper I need to repaint.
Would you repaint the whole bumper, or is there some way to 'fade off' the spray effectively?
In some cases, it may be acceptable to do only half of the bumper. Color changes in the middle of the bumper are usually less visible than at the sides of the bumper.
When I had bumper damage, my bumper was repaired and half of it was repainted. The result was entirely acceptable. No complaints about differing paint color.
If the car is really old, you should consider that the color of the car can change as a function of time, and therefore using new paint of the same color in an old car may not lead to the desired result.
If the final paint coat is only paint then it should be possible, but if it has a colour coat finished with a lacquer coat IMO you will need to do the whole bumper.
For the best finish, I would do the whole bumper - that way you don't have any colour mis-match or edges.