The 15-year-olds were standing on the number six bus to Clifton at Clarence Street, when a man sitting next to them stroked and squeezed their bottoms.
It is believed the man also assaulted other women on the bus on Wednesday.
He is in his 40s, with a moustache and stubble. He was wearing a black beanie and a black puffa style jacket.
Officers are appealing for information about the incident - which happened between 3.40pm and 3.52pm - and are asking other passengers, to get in touch.
They also want anyone else who was assaulted by the man to report it to police.
Call 101, and ask for PC1371 Ruth Atkins or email [email protected]