Our new bassinet and mattress was exposed to smoke from a fire for a few minutes before being removed from the area. Is it still safe to use when the baby comes or do we need to replace it? Our baby is due in 2 months.

Red Nose does not have specific guidelines about smoke from a BBQ or home fires, however, it is important to ensure the air quality for all, but especially babies, is good.
As far as any exposure to 3rd hand smoke (residual smell) it is generally accepted that if the smoke can no longer be smelled, then there is minimal, if any risk to baby.
Maybe give your bassinet & mattress some direct exposure to sun - this should remove any residual smell.