Roslyn Condie, of Mossdale, near Castle Douglas, admitted being the owner of a dog which was dangerously out of control last September.
A court heard how her Staffordshire Bull Terrier, Nipper, bit the postman on the leg leaving a puncture wound.
Sentence was deferred on Condie for six months.
Dumfries Sheriff Court heard how the incident happened while the postman was delivering mail in the village of Mossdale.
Local residents gave him first aid and he later had medical treatment for the bite.
Fiscal depute Jennifer McGill said there was concern in the area over the dog which had on occasion escaped from the garden of its home.
A solicitor for Condie said she had had the dog since it was a puppy and it was very affectionate.
She now kept it muzzled when taken out and the garden fences had been made escape proof.
Sheriff Brian Mohan handed out the warning that a second bite would bring destruction and deferred sentence on Condie stressing that she should keep the dog under control with appropriate measures.
A sheriff has warned the owner of a dog which bit a postman delivering the mail that her pet will be destroyed if it bites someone again.