Depends on a few things really,yea they can just paint that section but paint fades with age and unless its a brand new motor or freshly painted,chances are it will stand out like a sore thumb.
Most bodyshops would want to paint the whole bumper really,I would have when I had my place as it gives you good opportunity to blend into the panels.
It'll need plastic priming as well so budget on about £120-150.
You could try these "chips away" type smart repairers but generally their work is appalling compared to a proper bodyshop,dust under the paint,always seem to have a Matt finish as well,we used to correct their work on a regular basis.
Hope this helps.
A photo maybe useful too?