In a series of videos posted to social media, the convoy is seen matching and surpassing the speeds of surrounding cars as they drive and do wheelies on roads near the Sydney landmark on Tuesday afternoon.
The group seems to consist mostly of young men and at least one of the riders in the video appears to be wearing a school uniform.
One clip shows police attempting to stop them, before the riders breeze past the officer's motorcycle.
Police later caught up with the group at Mrs Macquarie's Chair and gave them a talking to before the riders dispersed.
"Joy rides on the Sydney Harbour Bridge are stupid, unsafe and a middle finger to the police and the community," NSW opposition transport spokeswoman Natalie Ward said.
"These kids know they are unaccountable and untouchable until there is compulsory licence plates, enforcement and accountability."
Ms Ward argues licence plates for all e-bikes would offer greater accountability.
"Labor keeps obsessing over wattage, speed caps and technical definitions," she said.
NSW Premier Chris Minns foreshadowed changes after his government rejected creating a reporting system for non-compliant devices and unsafe riding.
He also criticised Ms Ward for allowing high-powered e-bikes to be exempted from road registration when she was a cabinet minister.
"The current situation is intolerable and it's dangerous," the premier told reporters on Wednesday.
"It's regrettable that the original decision (by Ms Ward) was made to have a 500-watt output rather than a 250-watt output, because we're now in a situation where we're trying to close the barn door after close to a million of these machines are on Sydney streets.
"We'll have more to say soon."
In addition to being no more than 500 watts, e-bike batteries can only operate as a pedal-assist and cut out when the vehicle reaches a speed of 25km/h.
Anything that exceeds those power or speed limits must be registered as a moped or motorcycle.
Police already have powers to seize vehicles that are not road legal.
It said the Harbour Bridge convoy was seen riding on roads and there were no injuries or recorded damage to property, or vehicle seizures.
E-bikes, many retailing for more than $2000, and other high-powered vehicles have become a lightning rod for controversy in parts of Australia.
A teenage boy is awaiting trial for manslaughter after allegedly killing a 59-year-old while riding an unlicensed electric motorbike through a park in Perth in July.
At least 100 illegal devices were seized and 2100 fines handed to riders during a Queensland police crackdown in December.
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