how much money do the bush tax cuts actually cost per year?

Assuming that the cuts had no effect on the economy, they reduce what
the taxpayers pay the government by about $250 billion per year.
http://www.cppp.org/files/6/Backgrounder.pdf

However the cuts should (by any respectable economic theory) and seem
to have (based on evidence in the economy today) stimulated the
economy.  This boost in the economy created jobs which does several
things that put more money in the governments pockets (moreso in the
mid to long term than in the immediate term as Americans seem to be
stuck in all too often):
1) increases tax revenues (more people working = more people paying taxes)
2) decreases welfare payments (more people working = less people begging)
3) decreases medicaid (more people working = fewer people without health insurance)

There are certainly other effects on the economy, but those are the
more obvious ones.