That's what I was thinking. I don't think she will stop being Catwoman persay because she would probably help out Bruce and Batfam when needed. So I'm guessing they might just go with Bruce Wayne is married to the Catwoman, especially if she goes "goody-goody" in the public's eyes. Which technically wouldn't raise any suspicion because in the public's eyes, Bruce is Bruce and Batman is Batman and they don't know they are the same. And in the public's eye, they probably were not aware of a "relationship" between Batman and Catwoman. People in Gotham are not paying that much attention to these things.
I mean to be honest, people won't figure out that Bruce Wayne is Batman for the same reason they can't figure out that Superman is Clark Kent.