The shuttles costs are basically fixed at 1billion USD a year. Most of that is staff, launch pad and equipment costs. If you can fly 20 times in a year you'll start to make a profit. The problem is that the shuttle needs a lot more post landing maintenance that was envisaged.
Of course, this was the original plan for the space transportation system but it never worked out like that.
Even 1.3 billion, that was the last number I had in mind, for a flat number of six flights per year. Six flights more in a year would only add around 500 million USD, but require additional investments into the ground infrastructure - and turn the 1.3 billion for the first six flights into 1.5 - 1.6 billion USD per year, because you have more hangars and more ground vehicles, as well as more employees to pay.
Never forget: The spacecraft, even the launch vehicle, is just the peak of the iceberg. The part you see in TV is only the most visible tiny contribution. The real magic happens outside your view. Even the VAB is tiny compared to the part that plans flights, calculates budgets, trains astronauts and handles the whole kilotons of paperwork that have to be produced for each flight. If you see SRB segments arrive at the VAB, try to imagine how much effort was behind making sure that these segments after a few thousand kilometers of travel arrive right on the time they are needed. That is a whole lot of phone calls behind that single event.
Which is why complaining about money being wasted for space is extremely stupid: The money is spend deep down on Earth, and the people that complain loudest are always those who usually defend the trickle-down hypothesis - as long as it tickles down from their own bank accounts.
Around 230,000 people are still needed every year for making the Space Shuttle run. Only around 15,000 of these are employed at NASA or USA. The rest are the various subcontractors, outsourced specialists, military and just lowest-level service workers. Or do you think astronaut trainees clean up their own vomit after a centrifuge ride?
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If you want to operate a private space plane, you need to scale things down a lot and remove a lot of "committee decisions". The Space Shuttle is a great 1970s spacecraft with some small updates, but if you need to get the most bang out of every buck you spend, you would not decide the same way as the NASA people did. For example the on-board computers have actually been badly obsolete when the Shuttle was designed, the AP-101S update later made it at least comparable to other radiation hardened computers of that era. Today you wouldn't use it, you would get a standard satellite computer from the shelf, using radiation hardened chips that are maximal 3 years old at the time the computer was designed (The AP-101 was already used in Skylab, think about it). Also you wouldn't throw so many different technologies together only because they are common to the people who have to build and operate the thing.
A private Space shuttle would also do away with the payload bay for the next 30 years. It was too soon for this, a smaller EVA platform with some small payload mounting points would be good enough. The whole spacecraft could maybe be weighting just 35 tons (wet launch mass) at the end, still carry seven astronauts, have still room for docking port or external airlock, and still have a RMS. It could have a launch escape system.
The question is: Can you sell such a thing to customers? The price would also depend on how many such spacecraft you build. if you just assemble have a dozen of them, it doesn't pay out compared to expendable vehicles - in the time until you need to provide the next generation of it, you can't do enough flights to justify the increased R&D and manufacture costs.
