He expanded Medicare to cover prescription drugs, created No Child Left Behind, fought for Immigration Reform, and insisted on Islam as a religion of peace.
One of those things would get him called a moderate. All of them make him a RINO. Even with his hawkishness, social conservatism, tax cuts, and SS privatization attempt.
I'm not very qualified to say if someone is conservative or not, but I disagree with that analysis. It's important not just what issues are being tackled but also how they are being tackled. Most Republicans don't want to scrap medicare, so incremental reform isn't out of the realm of possibility - especially when the method of that reform is a mixed public-private solution. NCLB was an unfunded mandate meant to enforce standards on schools that were deemed to be "failing," using punishment as a tool to incentivize improvement. And as for Islam, just because Trump and Cruz are lunatics, doesn't mean the whole party agrees with that. A lot of them don't. Though I'll give you Immigration Reform. He definitely took a lot of heat from all sides for that, but I think he just genuinely believed it was the right thing to do.
Anyway, have to remember that Bush also wanted a constitutional amendment banning same sex marriage. He might be considered too liberal by tea party loons, but I think most conservatives would be fine with him.
He would do well with the establishment wing, the social conservative wing, and the neocon wing, even if he wouldn't appeal to some of the hardest Trumpists.