Mary Houghton, 73, had been walking her dog in Hambleton Park when she was approached by Geoffrey Haworth.
When Mr Haworth attempted to speak to her she became "petrified" and got in her car.
As she drove off Mr Haworth's legs became trapped under the vehicle. He pulled himself up on to the bonnet of the moving car where he stayed
before falling off.
Houghton, of All Saints Road, admitted dangerous driving at Preston Crown Court where judge Edward Slinger told her a motor vehicle was "a potentially lethal weapon".
Julian Harris, defending, told the court: "She had driven for 56 years without blame until this catastrophe last December.
"The last few months have been a great trauma for her. She is deeply upset at being at court."
The court heard Houghton was said to be on edge about being approached by strangers in the park.
When asked if she thought her driving had been dangerous, Houghton said she had no choice as the man had been holding on to the car.
She explained she had driven very slowly while the man was on the bonnet.
Mr Haworth suffered considerable pain to his legs and needed hospital treatment. It was some time before he felt able to walk again.
Mr Harris said his client was highly regarded in her local community, had no previous convictions and the loss of her driving licence would be catastrophic for her.
He added: "She feels genuinely ashamed of what has happened. She asserts that she would never deliberately hurt anybody.
"When the man ended up on the bonnet, she essentially panicked."
Houghton was ordered to pay £643 costs and a £15 victim charge. She was banned for five years and fined £750.
She will also have to take an extended re-test before she can drive again in future.