The incident happened whilst the bus was stationary on Ludlow Road, just before 10pm on Saturday 26 September.
The victims, a 26-year-old man and a 43-year-old woman, were waiting to leave the number 3 bus when they were both assaulted by a drunken man.
They both received facial injuries as a result.
The man is described as white, large build, and in his early 30’s. He was wearing a pale blue sweatshirt with jeans.
If you recognise this man, or have any information that may help our investigation, please contact 101 with the reference 44200374537.