Around 130 people had gathered on Tuesday evening to protest against the Government's Police, Crime, Sentencing and Courts Bill, which will see the police handed new powers to tackle demonstrations.
It comes just two days after another protest in the city descended into rioting.
Shortly before 11pm last night, police said protesters had been moved off College Green but that a "significant number" remained on Deanery Road "and continue to refuse to leave the area".
The force tweeted: "Officers will take proportionate action to disperse crowds. They are not containing anyone and we continue to urge people to move on."
About 90 minutes later, police reminded the public that gatherings were not permitted, adding that demonstrators "risk spreading the virus further".
A later statement said 14 people were arrested for offences including breaches of Covid-19 legislation and obstruction of a highway, with one arrest in connection Sunday's violent disorder.
Chief Superintendent Claire Armes said: "Officers had engaged with protestors and asked them to disperse, but tents and a sound system were set up so it was abundantly clear they were intent on remaining at the location, in spite of legislation in place to protect public health.
"After the scenes of violence witnessed in the city at the weekend it was necessary to bring in additional resources from our neighbouring forces to ensure the protest was safely brought to a swift conclusion.
"Throughout the operation officers continued to urge protestors to move on - at no time were they contained - but there came a time when enforcement was necessary as gatherings are still not permitted."
A YouTube livestream appearing to be from the demonstration showed large numbers of police with some officers on horseback and others with dogs.
Shouts of "Our streets" and "Shame on You" could be heard.
Chf Sup Armes said: "It's disappointing that officers needed to take this action on a day we should be remembering all those who've lost their lives to Covid-19 over the past year.
"The communities of Bristol have made too many sacrifices and worked so hard to defeat this virus, it's unacceptable for people to insult their efforts in this way."