Tyler Cowen explains why he thinks Milton Friedman favored bank bailouts. I find this much more plausible than the alternative view that he thought the Fed should have let the banks fail, and then substituted for the destroyed demand deposits by printing physical currency.
That's because this idea seems fairly silly. The velocity of money was falling rapidly, which is to say that when people got their hands on money, they were holding it, rather than spending it. Printing physical currency in the massive amounts that would have been required, assuming that it did not trigger further financial hysteria, would simply have given people more money to put under their mattress. As far as I can tell, the only way to get that money into people's hands without creating further panic would have been expansionary fiscal policy, which the Fed didn't control. The Fed also did not have the authority to take the country off the gold standard, which would have been required to start wildly printing hard currency.
Money supply is always, in some sense, a proxy for functioning credit markets. If a third of the banks fail, trying to put the lost money back into the system by open market operations makes little sense. Randomly distributed cash will not restore the confidence lost when perhaps a quarter of the country sees its savings wiped out.