Atkins was bought in to oversee work by main contractor Bam Nuttall who are currently involved in a legal row with council bosses after the project came in £64m over the original £87m budget and two years late.
The council has set aside millions for a legal fight with Nuttall if it cannot reach a mediated settlement.
It believes it owes Nuttall the £87m original fee plus any differences for delays and alleged defects.
Nuttall said the project cost £151m to build and wants full payment.
Commenting on the Atkins bill, Bob Menzies, head of busway delivery at the council, told the BBC: “Bam Nuttall finally delivered the scheme two years late and now dispute they should be liable for the overspend as set out in the contract.
“The council has no choice but to bring in extra resources to manage the contract and make sure that Bam Nuttall’s claims are properly assessed.
“To make sure best value is delivered for Cambridgeshire taxpayers in the long run, the council must take the correct advice, which comes at a cost.”
Nuttall has consistently declined to comment on the case and Atkins did not wish to make a comment.