Your proposal sounds like a great way to get excellent bail services for people who have money, but that’s not how the courts are supposed to work.
Sure about that? The way this country is heading is "One dollar = One vote". And once a sector gets accustomed to a stream of cash, there's no way to stop that flow of money.. No matter how dirty that money is.
More fundamentally though, these sorts of "free market" theories tend to assume an unreasonable amount of options and knowledge of potential clients. See: payday loans. Sure, in theory all the details of the loans are pre-agreed, and customers sure do have a lot of options. In practice, the most ethical providers tend not to be the most successful.
If not, and you feel like contributing to the dystopian hellscape we live in: business oppos!
Well, that's something to think about, then. It wouldn't even necessarily just have to be between the suspect and the bondsman; you might also allow judges to allow bail contingent on the suspect wearing a locating device.
Private bail bonds are an almost uniquely US phenomenon. Most other countries either go harsher and keep everyone awaiting trial in jail, or more humane and allow bail on conditions not money. Only America sees it as an opportunity for economic exploitation.
The best way to wither the system would be to speed up court proceedings.
The thing is, there's only one county court. If the county court has a program of ankle bracelets and text messages and supervised release and that program doesn't work, there's no incentive for it to change. And there's no alternative for the suspect, either--the judge has final say. With cash bail, there might be a dozen bail bondsmen in the county all in competition, each with the incentive to provide competitive terms to the suspect while guaranteeing their presence at court.