The month after Bronson took office, he revoked a paid parental leave policy for city workers. Another policy was revoked that allowed un-unionized city workers to bring their young children (up to six months old) to the office. Both policies were enacted by the previous mayor Austin Quinn-Davidson late into her term. Bronson cited the lack of research on the policies prior to implementation and their rushed nature approval as reason for their dismissal. He also said that he received complaints from workers about children brought to work.

During the COVID-19 pandemic, Bronson has declined to enact mask or vaccine requirements, saying that it was a matter of personal choice. He also said he would not get a vaccine, calling it "experimental". During an Anchorage Assembly meeting on September 29, 2021, he defended the use of Star of David holocaust imagery worn by those opposed to a municipal mask mandate. The mandatory mask ordinance–requiring any individual older than two years old–to wear a facial mask indoors was debated at the meeting. Mayor Bronson initially advocated for the symbol’s usage, calling it a “credit to [Jews],” but later recanted the statement after public criticism. He went on to say that although he agreed with opposing the mask ordinance, that protestors should choose a different symbol to do so.

On October 1, he ordered a stop to water fluoridation in Anchorage based on reports of dangers such as burning eyes and throats of workers. Bronson's response was criticized by the representative of the workers, Aaron Plikat, who claims that they had never complained about the fluoride. He allowed it to resume when he discovered that it is mandated by Anchorage's municipal code, and no significant impact on the water fluoridation level was caused on October 1, 2021.

In May of 2023, Bronson closed the homeless shelter at the Sullivan Arena leading the homeless encampments in Anchorage parks to "explode in size". Bronson said that the Arena should go back to hosting concerts and hockey games, and suggested sending the homeless people to Los Angeles and other cities in the Lower 48. Bronson had made plans to construct a new shelter for up to 200 people, but the Anchorage Assembly shut down the project. Construction had begun without finalizing funding and without a plan for its operating costs going forward.