No, it's not from thin air. Bridge financing is from cash on a bank's balance sheet (or as mentioned above, sometimes non-bank entities). Banks usually participate in bridge financing (some fees, loan on balance sheet typically on a short-term basis) because they want to also be part of syndicate financing (more fees, previous loan syndicated out to investors).

Banks infrequently get "hung" with loans and these usually are just bad deals that somehow got through. There are more hung loans now on deals that might have been okay under normal economic circumstances but are not feasible right now.