I'm not quite getting whether you mean would his parents be proud of him? Or that the issue is whether or not society in general thinks well of Bruce Wayne.
I think the man he is encompasses his entire self, not just one aspect. And that his parents, depending on your view of the afterlife--if they are feeling one way or another about him, can see the whole person.
If you mean that say... people who knew his parents think Bruce Wayne is a silly man, I think Bruce is strong enough to live with that. He's proved he's above worrying about what people think.
He and the people he cares about know the truth. And even if he is sometimes portrayed as silly, it's part of his disguise and he's still managing to be a philanthropist, a businessman and raise good kids.
That's enough, really. Any person who can do that--that's pretty darn good and better than a lot of people tend to do. Even without the Batman part. I'm not getting why that's somehow embarrassing or shaming to his parents (if that's what you're saying) when it's a purposeful disguise and is really just a little silly, not anything terrible.
This is not to say Bruce is not a huge philanthropist in his "Bruce Wayne" persona but I'm sure someone with his brains could be a major world figure without having to resort to making Thomas and Martha's legacy (in most people's eyes) a wastrel, a playboy and a fop.
I think it's a matter of focusing on the mission instead of what other people think. Bruce has personal integrity, and I think that's nobler than worrying what people think.
Also, Bruce Wayne!Socialite is not that terrible. A little silly. Everybody has eccentricities, and some might say the very wealthy have more eccentricities than others. They can afford it, I suppose. It also helps him keep his secret identity.
I don't think it would be helpful to the mission for Bruce to become a political world leader. I think it would be mixing too much politics in (and that Bruce would see that as unethical) and he already is pretty busy being a world leader as Batman--both in Gotham and all over the world and with the JLA. Plus running a company and having movie nights with the kids and pretending to be a socialite.
I don't think that Bruce Wayne has anything to be ashamed of. I also think Tommy Hush is going to crash and burn and make Bruce Wayne look much worse than real Bruce Wayne ever did.
i.e. that a man of his genius and abilities and resources could do so much more for the world (and Gotham) instead of spending billions on Bat-toys and spending much of his time in a cave.
I'd prefer Bruce not mix his mission with politics, and he is a world leader already. He can't, actually, spend all that much time in the cave if he's as busy as his multiple books and other people's titles suggest. And using the word 'toys' I get, but to me, 'toys' is the wrong word. They're tools. Tools that help him and his team stay safer and be stronger more capable in their fight for good. He's not a metahuman, Tim and Dick aren't, so he invests in (and himself builds and invents) tools that help them all, and consequently Gotham, the Justice League missions and members, and his life work.