The insides are never well finished Phil, and even a rechroming won't provide long term protection. When I had my front MGB bumper rechromed many years ago I asked about a guarantee and the chromer just laughed!
Remove your bumper from the car. Protect the outer surface - masking tape or similar, and place on an old towel. Then probably a drill attachment will be best on the rust first - use eye protection.
Then follow Martyn's advice with a rust converter if necessary. Follow that with an etch primer. When that's dry - my favoured finish is just silver paint - wheel paint will work, as will any standard silver. Originally they seemed to have had a rough hammered silver finish, which is not easy on the eye.
