The man is believed to have sat next to a 24-year-old woman and touched her inappropriately.
She was travelling on the X51 service from Birmingham to Walsall. After being challenged the man fled from the bus in Perry Barr.
He is described as a fairly dark skinned Asian man in his mid 40s, of average build and around 5ft ins tall with white facial stubble and a scruffy appearance.
He was wearing a baseball cap and carrying a rucksack with a Union Jack on it and he spoke with poor English.
Det Sgt Emma Holder said: "This assault has traumatised the young woman who was just going about her journey. She had the courage to challenge the culprit who then made off, however it has left an emotional scar on her.
"Anyone who knows who he is should come forward so that we can fully investigate."
Anyone who recognises the man on the bus should call Det Sgt Holder on 101 or Crimestoppers on 0800 555111.