Appeal Court judges rejected claims that the decision to issue an environmental permit for the development was compromised by a fundamental scientific error.
Local campaigners insist there is a risk of toxic heavy metals from the plant at Rookery Pit, Stewartby, finding their way into drinking water via the River Ouse.
But scientists from the government-sponsored Environment Agency insist there is no such risk and and the court rejected claims that their stance is irrational.
The plant, known as Rookery South, is a nationally significant infrastructure project and Covanta Energy was granted development consent for it in 2011.
The permission was subject to a legal challenge, but the consent was finally upheld by the Court of Appeal in February 2015.
Campaign group BACI Bedfordshire challenged the environmental permit which was granted in January last year.
It insisted that there is a threat of toxic dissolved heavy metals being discharged from the plant into Stewartby Lake, 500 metres away.
The lake is connected to the River Ouse, which feeds the supply of public drinking water.
BACI claimed the permit was issued on the "factually incorrect and scientifically erroneous basis" that measures adopted for dealing with fugitive emissions from the incinerator bottom ash would prevent the discharge of heavy metals.
Covanta and the Environment Agency conceded that there was an error in a single sentence of a supporting information document.
But BACI's judicial review challenge to the permit was rejected by a High Court judge last year on the basis that the error had not affected the ultimate decision.
Mrs Justice Lang found that the permit would be effective in preventing the discharge of dissolved heavy metals into the surface water drainage system.
She acknowledged that there was a "fundamental difference of opinion" between experts as to the risks of surface water contamination.
But she said the Environment Agency had made it "abundantly clear" that, in its view, there was no such risk.
And the judge rejected claims that that conclusion was "irrational, or based on incorrect science."
Dismissing BACI's Court of Appeal challenge to the judge's ruling, Lord Justice Lindblom said he could detect no flaw in her reasoning.
The crucial issue, he observed, was whether the error in the supporting information document influenced the Environment Agency's decision to issue the permit.
And he concluded: "To this question the answer is, in my view, clear. The error did not affect the Environment Agency's determination. There is no evidence to show that it did."
Both the permit itself, and the reasons given for granting it, showed that the Environment Agency had grasped the relevant science.
And its conclusion that contaminated water would be successfully contained in a sealed system, thus preventing pollution, could not be characterised as irrational.
Lord Justice Lindblom, who was sitting with Lords Justice Henderson and Peter Jackson, also noted that it was no part of the court's role to substitute its own view for that of the Environment Agency.
Mrs Justice Lang had rightly afforded a "margin of appreciation" to the Environment Agency's exercise of its expert scientific judgment, he ruled.
R on the Application of BACI Bedfordshire Limited v The Environment Agency & Anr. Case Number: C1/2018/2968