A reader writes:
I think there might be a simpler explanation than that: Bush has stayed out of the Islamophobia debate because he's stayed out of everything. There is a school of thought that this is exactly how a former president should behave. It's not one I completely agree with, but it's one I understand and respect. It's also the same route his father took. (The only time I can remember George HW saying anything publicly after his presidency ended was in a charitable venture in the aftermath of Hurricane Katrina.)
In applying Occum's Razor to Bush's silence, I don't think Thoreau is working hard enough. His theory would suggest a willingness to speak out about things that do bother Bush that the former president hasn't demonstrated to date. Consider that the only two significant quotes to come from Bush since leaving office are the "I'd do it again" quote you referenced, and his "He deserves my silence" response to attempts to draw criticism for Obama's choices. Both of those came from Q&As at speaking appearances. In those instances, he wasn't speaking to the media, but directly to people or a moderator as part of a discussion.
So the simplest explanation would be that Bush is not inclined to just grab a bullhorn and pronounce, and, as a corollary, that he doesn't want to be involved in public debate any more. Laziness is always the simplest explanation!