OK, you posted a pic, but it's practically useless for identification purposes. I need to see the side view and a view of the bottom close-up to see if I can identify the maker. Post more pics. If I can identify it, we can find a replacement.
My bad: OK, I looked further. The sides of the bowl have no distinctive impressions. Are there any markings at all on the bottom of the bowl? I can't see any from the pic Also, you say it's a nested set. So, what color are the other bowls?
Well, without markings or distinctive identification, I'm at a loss to help any further, sorry.
But they don't appear to have a lot of age (vintage or antique), so I'm going to agree with the other posters and say that most grandmas wouldn't care much about the loss.
I think if you apologize and offer to buy a new set of salad bowls, she'll be satisfied with your efforts. You could ask where she bought them, or offer to take her shopping for new bowls. Good luck, anyway.