Do you think he would stay quiet like Michelle is doing or would we see him in front of the cameras any chance he got?
Well, I don't think you can point to Mrs. Obama being quiet, because she had sparked quite the intense conversation about food and fitness in public life and government's role in that.
That being said, I think Bill will have a larger presence than previous spouses, but not without incredibly careful negotiation. Some of this, I think we can be safe in saying this, is going to be due to a double standard for men in public life. We will not put the same emphasis on the spouse's public profile that we would on a woman.
That being said, Bill will present new challenges that a less accomplished man would not have to go through. For one thing, people are incredibly worried about a co-presidency, given that Bill is still a popular, gifted politician who already had 8 years of Presidential experience. While the First Lady's office has continually evolved and expanded in prominence, Americans are still wary of having to weigh even more factors beyond their immediate control. We have some difficult dialogue in determining the proper role for the Vice President, but we have fairly explicitly voted on a Pres/VP ticket for quite a while. We haven't had the same public dialogue with either executive figure's spouses.
What the First Lady's office has expanded to is the social consciousness of the nation. In this regard, Clinton's post-presidency work is well-suited for this purpose.
I think Bill, by virtue of who he is, will have additional media attention and gravitas without any intentional plan in mind. That being said, he has to deal with making sure that he will not be a distraction to Hillary's Presidency and will not create an incredible unease about the status of his future leadership in the Office of the First Lady (which would of course be renamed).
Now, of course, my long-standing conviction is that unless something dramatic happens, we will have a Republican in office. Americans have been very hesitant to elect the same Party to consecutive Presidencies. The only things that had stopped such developments were incredible wars (beyond what we experience in the modern era), an almost entirely chaotic Party coalition (any discussions about GOP civil wars pale in comparison with the Democratic Party of the late 19th and early 20th century). 1988 to me was almost an exception to the rule, but there was substantial difficulties in the Democratic Party (not nearly as bad as the William Jennings Byron era).
So I'm not really convinced we get to see this experiment in a female Presidency just yet.