When he got back to land, Mr Fletcher looked up and saw a man jump off the bridge after his dog.
Paul Wilson had been driving over the bridge when he saw Rosco in the water and decided he needed to help.
He pulled over to the side of the road, crossed to the middle of the bridge and jumped in after the dog. "He looked like he was in a bit of trouble so I started swimming out. When I was swimming, I started getting pulled out. I was about 100m out from the Matapihi side when the emergency services came out. The chopper turned up and made sure I was all right."
Mr Wilson said he was fine as he was a competent swimmer and he just lay on his back when he began being pulled out, until he was able to make his way closer to shore.
"I knew I wasn't going to get into trouble."
When asked why he jumped in after Rosco, Mr Wilson said he had dogs at home.
"You help a drowning animal as long as you don't become a statistic yourself. I knew I wouldn't become a statistic by saving someone's dog."
Rosco managed to get to shore by himself and was still energetic after his swim.
Mr Fletcher said he thanked Mr Wilson for his help when the two men met on shore.
Tauranga Fire Brigade senior station officer Len Sabin said when the emergency services turned up, there were two people in the water.
"The Coast Guard had been mobilised but didn't have a vessel in the area. We put a mayday out to vessels in the area but there were none around. So, basically, we had a local fireman who had a canoe handy and we also stopped a car with surf boards on board. We also had a couple of firefighters in lifejackets."
Mr Sabin said by the time the crews had scrambled together vessels and made their way to the men in the water, the Trustpower TECT Rescue Helicopter had also arrived at the scene to help.
"But the men were already in shallow water. They were lucky they were able to get out of the rip stream before it pulled them further out into the harbour."
Graeme Robins was driving across the bridge when he was stopped by the fire brigade, who asked to borrow a surf board strapped to his roof.
"It was awesome to be able to help out."
Tauranga Police said in a statement that a police officer had also jumped into the water to help when he believed Mr Wilson was in trouble.
Senior Sergeant Shannon Clifford said he was pleased all people involved were safe.
"The current was extremely strong. Our police officer, also a triathlete with strong swimming ability, did a very good job meeting up with the man, keeping him calm and assisting him back to shore."