The fact that government bears such a huge responsibility for the current mess means any response should eliminate the conditions that created this situation in the first place, not attempt to fix bad government with more government.
The obvious alternative to a bailout is letting troubled financial institutions declare bankruptcy. Bankruptcy means that shareholders typically get wiped out and the creditors own the company.
Bankruptcy does not mean the company disappears; it is just owned by someone new (as has occurred with several airlines). Bankruptcy punishes those who took excessive risks while preserving those aspects of a businesses that remain profitable.
In contrast, a bailout transfers enormous wealth from taxpayers to those who knowingly engaged in risky subprime lending. Thus, the bailout encourages companies to take large, imprudent risks and count on getting bailed out by government. This “moral hazard” generates enormous distortions in an economy’s allocation of its financial resources.