In 2005 Bush should have picked the best qualified of the Hispanic candidates — probably Emilio Garza — and nominated him and taken his chances with a filibuster. Or he could have nominated the ever-cooperative Alberto Gonzales with the specific expectation that he would be borked for the team. That would have put the Democrats in the position of having to attack and filibuster a Hispanic nominee, costing them support in that community and making the administration and the GOP look like they were the ones fighting for the advancement of minorities in government. Even though the nomination might have been blocked, the result would have been an enormous boost in popularity with Hispanics for the Republicans and a ding on the civil rights record of the Democrats. It's also entirely possible that the Democrats might have been bluffing and would have backed down to avoid seeming hostile to a Hispanic nominee.
As in other situations, Bush played politics like an amateur and failed to push what should have been an obvious advantage; the Republican party is still paying the price of that mistake. If Bush had played the situation the right way in 2005, then today Sotomayor would not enjoy the immunity conferred on the first Hispanic Supreme Court nominee, the GOP would be stronger overall, and might be able to oppose Sotomayor if their ideological concerns are strong enough. But as a weakened party desperate to be liked, the GOP may very well have to bite the bullet, sacrifice principles again and roll over and accept Sotomayor despite her troubling record. And yes, you can blame Bush for it.