West Yorkshire Combined Authority - who are leading the work to create a new multi-million pound facility - say their team have permission to continue work away from where the bones were discovered.
They do not know yet whether the find will cause a delay to the redevelopment.
As reported by the Courier, police were called to the site off Winding Road on Friday afternoon after what is believed to be human bones were uncovered.
Officers said the area was a burial ground before the bus station was built.
They are now working with the coroner's office about the discovery.
A West Yorkshire Combined Authority spokesperson said: “We are in contact with the police and the coroner’s office. Our contractors are not working in the immediate area where the discovery was made, but they have been given permission to continue works elsewhere on site.
"It is too early to say what impact there will be, if any, on the timescales for delivering the scheme.”