So the public transport authority stops running their own vehicles, and instead places tenders for individual routes? And anyone can bid on operating the route? I mean they already do that with subcontractors for contingencies etc.

Overwhelmingly however it's cheaper to vertically integrate, and private operators have no interest in taking low profitability routes (which can often be very important due to second order effects).

I will contend that automated busses might change things here a bit though.

Busses cause nuisances so routes are regulated. It is also difficult to operate them at a profit. If you let the market decide freely on a per route basis most routes would disappear.