There are positive and negative aspects to both contracting out government projects to private interests and operating them directly.
On the one hand, the bidding process CAN keep costs controlled, however this is completely dependent on the honesty and integrity of the parties to the contract and the open-ness of the bidding process. The no-bid defense contracts to Dick Cheney's companies and associates during the war is an example of how outsourcing can go horribly wrong. Because the books of the government, unlike those of private business, are open to public scrutiny which can result in terrible political consequences, they have at least as strong an incentive to control costs as the private sector.
Since the West began its love affair with outsourcing to essential public service provision and infrastructure (trains, energy, ferries, etc) to the private sector, there have been nothing but scandals, a deterioration of the quality of service and skyrocketing costs for consumers. In the UK, in the place of a national railway that was once the envy of the world, they now have a patchwork of private trains. They're dirty, run down, never on time, a trip from point A to point B may require doing business with several private companies and partnerships, and the tickets cost ten times as much as before. To add insult to injury they are heavily subsidized by British taxpayers.
I favour a mixed economy, where the government uses a combination of private sector bidding for short term projects like construction, but directly supervises permanent public sector requirements, such as maintenance, oversight, regulation enforcement and service provision.
Of course, whether a project is open to private sector bidding or directly implemented by the public sector, the cost-effectiveness and quality should be determined by a strong regulatory framework, transparency and fairness.