I have 3 white cars. For such small issues, I just use a good quality round paint brush with long soft bristles available from a good art supply shop and a spray can of white paint. You will also need a can of good quality of paint thinner such as Sikkins or similar. Spray a good amount of paint into a clean container (I just spray the can into its cap). Then just touch up the black area of the bumper. You may need two coats to cover up the black. The thinner is used to wash up the brush and the container after you have completed the work. From 3 feet away it will be hard to notice the damage. Total cost less that Rs. 500.
Other wise you are looking ad a full respray of the bumper if you need for it to look like nothing happened to it. Cost about Rs.. 6,000 - 10,000