Mrs Adsett said some swimmers, as well as a number of surfers, stayed in the water and watched the visitor.
On the beach, people were snapping photographs and taking videos of the shark in action.
"It was just cruising up and down," she said. "People were just walking up and down the beach following it.
"A couple of girls kept swimming but then it got within a few metres of them and I think they panicked a bit and got out."
The shark was visible for about half an hour before it swam out to sea.
Lifeguard Shaun Smith said the two-metre bronze whaler was patrolling a 2km stretch of shallow water near the surf club.
Swimmers were kept out of the water for half an hour until the shark swam away. Lifeguards are keeping an eye out for it and will clear the beach if it returns.
Export lamb roasts that spilled from containers from the grounded cargo ship Rena have been blamed for attracting more sharks than usual into the shallows off Tauranga.
"I would think if you got a chance to eat some nice export lamb you'd be pretty keen wouldn't you?" Mr Smith said.
"If you were a shark I think they'd be right up your alley."