But Bush is the President, and he's the one who pushed through and signed the universal entitlement.
Incorrect. Bush pushed for complete privatization the health savings accounts and got creamed for it in the press and total rejection from the Left. Hastert supported it but couldn't get the votes. Then came partial privatization and HSA but that failed. The only thing that could get enough votes was to turn the Democrats' completely government supported prescription plan into a partial private option/government plan with HSA.
That's usually how things work in politics - start with a big plan and have to settle for a partial victory. Bush didn't start out wanting to spend a lot of money. Reagan faced the exact same problem.