How difficult is it to replace the bonding done on a tooth?

One of my teeth is bonded, and I’m getting whitening done at the dentist. The bonding, however, is the original off-white color. I did a little research and apparently, bleaching won’t take to bonded teeth—only natural tooth structure. So, the bonding would need to be replaced with the whiter color. My question is, how does this happen? Does the dentist just coat over the bonded tooth? Or is it more complicated than that?