"It's put a dampener on our wedding weekend. I'm incredibly embarrassed and disappointed at myself," Bird told reporters.
Police said a 30-year-old man left a pub in the north coast town on Sunday night and was caught relieving himself on a fully-marked police car.
A number of witnesses allegedly caught him in the act at 7.45pm on Sunday after he left a Bay St pub.
Bird fronted the media on Monday afternoon and said he did urinate in a car park outside the hotel on Sunday night after celebrating with family.
He said a police car was parked next to their vehicle outside the hotel but maintained he urinated between them.
"I stupidly and regretfully went to the toilet between the two cars," he said.
"I know it was a stupid and dumb thing to do.
"But I really want to emphasise the fact that I didn't intend to disrespect anybody and I definitely didn't do it on the car."
Bird - who has had several brushes with the law since 2004 - would not disclose how much he had been fined.
Asked if he would now give up drinking, Bird said: "I am definitely considering it."
Gold Coast boss Graeme Annesley said a club disciplinary hearing would be held later this week before reporting back to the NRL Integrity Unit.
He would not speculate on whether Bird would lose the Titans co-captaincy.
"We have the option to consider anything that is appropriate under the terms of the contract but I don't want to forecast what might happen," he said.
But he added: "It is to Greg's credit that he has publicly apologised and clarified exactly what took place.
"That will all be taken into consideration before a decision."
Any punishment may pale in significance to Bird's bride Becky's wrath.
"She was just disappointed, we had such a great weekend," Bird said. "She is quite upset."
Then there's the public ridicule.
Jibes came thick and fast at Bird's expense on social media with one wag tweeting: "To be fair many Birds have done worse to a cop car."
Before Bird's incident, four Titans players had been arrested in 11 months.
- AAP
