Even your math doesn't show a doubling of funding. The link you provided from the NIH's budget actually illustrates the point I was making.
If you look back at the other years included in that proposal, you can see the effective funding levels dropping, as the success rate, or the percentage of incoming grants that receive funding, decreases. If you look a little closer at the budget specifics, you can see that in previous years, even with the funding increases, the actual amount of money going to funding projects decreases. This is usually due to the increasing costs of all the other components of the budget.
I'm not trying to claim that the budget for the NIH was cripplingly low during Bush's terms, or at least not way more than it normally is. But the budget for the NIH hasn't actually gotten smaller since the 70's, until Bush's second term. To say that the Bush years were great for science is a hard claim to make. Science and research took the back burner to Afghanistan and Iraq, in large part, and to a host of other issues here at home. And some people think that's the right choice. I just don't agree.
On the other hand, in the first three months of this year, an additional $200 million was added directly to the grant funding portion of the NIH's budget, which is not reflected in the current budget, as it was awarded after that budget was released. Call me selfish, but I think research is important, and I like it to get funded. And it's being funded better now.