Under that definition, bail outs are a fundamentally great part of capitalism. "Bail outs" in general parlance almost always correspond with government propping up businesses that would otherwise go bankrupt.

indeed - however the different between bailing out your local barber and a bank is that when you bailout a bank the upside is contained, but the downside is spread, whereas with the barber, since barbers don't fundamentally engage in activities that allow for exponential gain the bailout is more directly given to citizens in the form of services, not captured by rich people.