So if you're "opposed to financial bailouts," as a libertarian, you're not for the market. You're saying that one scheme for governmental disposition is better than another. Of course you are entitled to that opinion but the sheer force of libertarian doctrine is not necessarily on your side. The general pro-market and anti-government arguments are not necessarily on your side. I think it is quite plausible for a libertarian to believe that the Fed is "less bad" than the bankruptcy courts and the FDIC.
The libertarian concern should be with the rule of law and with the long-term distribution of power. The bankruptcy courts and the FDIC are institutions established by law. The bailouts were the idiosyncratic decisions of Henry Paulson and Ben Bernanke. Moreover, the Paulson Plan that became TARP was a huge transfer of power to Treasury and the Fed. It also desensitized the public to huge government expenditures and deficits, with the result that the deficits projected for years far past the expected end of the recession are higher by hundreds of billions or even trillions of dollars than what was projected before.
I could go on at length. Perhaps Tyrone and I should debate this. Eventually, such a debate would come up against the basic empirical problem that we cannot observe the alternative history. But meanwhile it would bring up a lot of interesting philosophical and economic points.