It depends somewhat on the productivity of the firm bailed out. If we imagine that this firm contributes nothing to GDP, and bailing it out amounts to handing t

It depends somewhat on the productivity of the firm bailed out. If we imagine that this firm contributes nothing to GDP, and bailing it out amounts to handing the principals money to spend on consumer goods, this would be net inflationary. But if the bailout preserves or expands productive capacity for goods for which there is effective demand, my intuition is that there need not be inflation. This is the sort of thing that's very hard to discuss without a formalization of production functions, elasticities of demand, etc.