Stagecoach said the union had demanded a 9% pay increase that would be delivered in 12 months.
Mr Roe said: “Over the past three years, our Cambridge employees have had pay increases of more than 20% with inflation averaging under 14% over the same period.”
He said the latest offer would have resulted in no change to existing overtime rates.
Mr Roe said the strikes would not impact the busway or the wider Cambridgeshire region as an agreement had already been made regarding pay.
“Once again, I apologise to our loyal customers in Cambridge for the disruption, which will inevitably be caused by these unnecessary strikes,” he said.
“We urge the union to come to our negotiations with a genuine willingness to secure a deal that is fair for our employees, sustainable, and responsible to the communities we serve.”
The union said it would “escalate” strike action if the dispute was not resolved.
Mark Plumb, its regional officer, said: “The disruption that will be caused to passengers is entirely the fault of Stagecoach for refusing to put forward a reasonable pay offer.
“There is still time to call the strikes off, but for that to happen Stagecoach must come back with an offer that is acceptable to our members.”