Crown prosecutor, Mr. Nicholas Newton, told the bench that WPC Sharon Gibby and another police officer saw Mandy Anne Nation, of 5 Holloway Court, sitting on a pavement on The Norton at around 10.10 pm on November 9.
When they inquired if she was all right, Mrs. Nation became abusive, telling the officers that it was "nothing to do with them."
Her purse and its contents were on the floor beside her, and Mrs. Nation again became abusive when WPC Gibby went to pick them up.
"Officers were of the opinion that she was drunk," said Mr. Newton. "She was asked to keep her voice down and to stop swearing - particularly as there was another member of the public walking her dog nearby who seemed alarmed at the situation - but she continued to shout in a disorderly manner and rant on."
Mr. Newton further explained that Mrs. Nation was helped to her feet and was taken to Haverfordwest police station in a patrol car.
During that journey she continually shouted at the driver that he was going too fast and at one point put her hand on his shoulder.
The police car had, said Mr. Newton, been travelling at between 50 and 55 mph.
Defending, Mr. George Allingham felt it had been a "misinterpretation of the situation by the police."
His client had not "fallen over drunk" but had slipped off the pavement, dropping her purse on the floor.
"However, she accepts that she was less than complimentary to the police and was less than co-operative," he said.
"On reflection, she admits she should not have been, and that her behaviour was inappropriate."
Turning to Mrs. Nation's behaviour in the police car, Mr. Allingham said that it was often the case that back-seat passengers had a different perception of speed and that to them "on some roads between here and Haverfordwest 50 mph might seem too fast."
In addition to fining Mrs. Nation, magistrates also ordered that she pay £40 prosecution costs.
A charge of being drunk and disorderly against Mrs. Nation was withdrawn by the prosecution.