The 39-year-old had met the man around the Waterloo Street area of Glasgow and they walked together from the city centre.
They went over the pedestrian-only crossing known as the "squiggly bridge' and along the Clyde Walkway.
As they approached River-view Gardens, in Govan, at about 2:30am yesterday, the man pulled the woman into bushes and subjected her to a serious sexual assault.
The man then ran off towards the city centre, leaving the woman extremely distressed but not physically injured. She told a passerby, who alerted the police.
The only description of the man at this time is that he is white and was wearing dark clothing.
Detective Sergeant Frank Clarke, of Govan CID, would like to speak to anyone who may have seen the man and woman walking across the bridge and on to the Clyde Walkway.