First, the very first TEA party protest WAS aimed at George W. Bush. The February 27th 2009 Tea party Protests were in part against the TARP bill signed by GWB.
Second, while spending has quickly became an equal if not greater focus the original focus was much larger on taxes, such as the second TEA Party protest held on Tax day that was focused singularly on taxes. George Bush, for all his issues that consevatives had on him, was pretty decent with taxes. On the flip side, Obama had already made statements at that point about letting the Bush Tax Cuts expire, talked about the notion of possibly raising taxes in general as being necessary, and had begun to raise other taxes not counting the income tax. So the notion that it was at the very least likely, if not garaunteed, that inevitably taxes would be raised was much more prevelant under Obama than under Bush.
Third, the Tea Party is about 50% "republicans" and about 50% independents, libertarians, and democrats that are conservativel eaning. The latter half WAS extremely critical openly of Bush and spending during his term. The other 50% had a large portin of them being also critical of Bush during his years but less loud and vocal. To be upset about this and ONLY focus ones anger or indignation towards the tea party is laughable and disingenuous though. You can look at the Anti-War movement currently which is a relative blip on the radar compared to even 2007 despite Obama simply following Bush's plan in Iraq and actually ramping up in Afghanistan. You can look at the immigration movement and how relatively quiet they've been despite that the Obama administration has not done anything significantly greater than the Bush administration did. It is common in politics, as it is in every other walk of life, that when your guys are in power your issues with them are dealt with in more quiet and back channel ways because you DO want it fixed but you realize your issues with "your" guys would be even BIGGER issues with the "other" guys.
Fourth, there was a decent bit of conservative outcry over things like the perscription drug bill, no child left behind, and TARP under Bush. In regards to other spending things such as the War on Terror, there was begrudging acceptance due to at least believing that national defense is a legitimate government duty. The notion of buying car companies, providing health care, bailing out wallstreet, worthless "service" project funding, and other such things NOT being part of what the federal government constitutionally should be doing adds to the indignation.
Think of it this way. Lets say your family is strapped for cash. If your spouse goes out and uses what little money you have on food but gets relatively expensive name brand food instead of generic brands, you may say "hey honey, next time can you go for the cheaper alternative. Money's tight". You're not likely to make a huge fit about it though because hey, they're spending it on fooda nd you all need food. However if they instead go out and come back with a new dress and high heels, or with 3 XBox games, you're probably going to have a much bigger issue and much more vocal issue because they're using it on luxuries not its intended purpose.
Finally I'll point out that the Tea Party, since its formation and momentum, has NOT been focusing just on democrats. They HAVE been critical of Republicans, they HAVE gone after republican politicians. While the movement may've not been formed and loosely organized under Bush, using that as somehow a sign that this is solely a republican entity or something just born out of hate for Obama is a bit transparent when its obvious their issues are with a mentality and an ideological view point regardless of whether they see that view point in a person with a (D) or an (R) next to their name.