Bill Dewey displays some of the common stereotypes of politicians: he believes his position entitles him to certain privileges, he's overly concerned about money, he's distinguished in public but lacks confidence in private (especially when put under any pressure), etc. He likes to pretend that he has more importance, influence, and control over Beach City than he really does. It is also implied that Bill has made some less than legal choices during his career as mayor.
He refers to the town as "a magnet for disaster", which is a fair assessment as the local is often the target of unnatural phenomena such as dangerous Corrupted Gems, destructive machines from space, and other disasters like the recession of the ocean or the falling debris from the Gem Warship. He's slightly incompetent at his job of managing the city (he pitifully tries to refill the ocean with a watering hose when it recedes), so he employs a "bread and circuses" political tactic to keep himself in the town's good favor. He believes it's his job to keep the citizens feeling calm and secure, so he often sets up various diversions and attractions such as the world's largest bowl of ice-cream ("Joking Victim"), a Summer Season welcoming speech ("Mirror Gem"), a New Year's Eve fireworks show ("Maximum Capacity"), and a statue of himself.
He visits It's a Wash to have his campaign vehicle cleaned in "Cat Fingers". He is upset when Steven sprays him during a hose fight and tells Greg to control his kid. Greg apologetically says the car wash was free, and Mayor Dewey seems satisfied.
He later makes an appearance in "Lars and the Cool Kids" where he is seen giving a reelection speech and kissing a baby as Sour Cream, Jenny, Steven, and Buck Dewey drive by in Jenny's Car.
He appears in "Joking Victim", when he presents the biggest ice cream bowl in Beach City. When Lars burns it with the Fire Salt, he seems to be unaware that it could melt.
In "Mirror Gem", Mayor Dewey is first seen driving on the boardwalk, which Steven happens to be walking on. After telling him to "go get run over somewhere else", Dewey drives to the ocean-side, where he makes a speech to the people of Beach City about the coming of summer. Unfortunately, his speech is full of double entendres, which Steven and The Mirror mock in order to make fart jokes. The audience is more entertained by Steven’s antics than the speech, leaving Dewey mildly put off.
He appears again in "Ocean Gem" on the beach and is panicked over the sudden disappearance of the ocean. He's seen grieving about the resulting damage that's likely to be dealt to the city tourist industry, as well as the likely end of his career. After Steven and his friends return the ocean, Dewey desperately yet thankfully embraces Steven as the rest of the townspeople celebrate his heroism.
He takes on a main role in "Political Power" after the Crystal Gems accidentally knock out all the power in the city with an EMP. Enlisting the help of Steven, he travels around the town assuring the citizens that everything will be fine and that the power will return that night. After the power doesn't return the citizens of Beach City turn on him for lying. He is quickly saved by Steven who encourages all of them to stay strong and to not turn on each other. He also gives Steven advice and explains to him the basis of politics, which, as he understands it, is making stuff up to ensure that the citizens of the town are kept happy and safe.
He returns again in "The Return" after being called by Steven, shown cowering behind a curtain in response to Peridot's ship. Steven calls on him to use his political powers to convince the citizens of Beach City to evacuate to keep them safe from the approaching threat. He is later seen driving around town with a new truck jingle urging the citizens to evacuate. After Steven is knocked out of Greg's van from the airbag he is seen standing around with the rest of Beach City's Citizens making sure that Steven is not hurt.
In "Shirt Club", he is seen unpacking inventory in the Abandoned Warehouse, and practices "acting cool" in front of Buck but always fails. He made a poster for "Bench City" (which was actually just a poster that says "Welcome to Beach City" re-written into "Welcome to Bench City" by Mayor Dewey in permanent marker.) He is rushed out of the Warehouse by Buck and is later seen again, giving a speech about the bench that was positioned behind him. He is shot in the stomach with a T-shirt by Steven as his body guards and the whole crowd goes wild and runs in different directions as they see T-shirts randomly being shot out from nowhere.
In "Historical Friction", he writes the play about William Dewey originally before Pearl fixes it. Later, while the play is being presented by Steven and Jamie, he realizes the script's been changed and he's worried at first until the townspeople enjoy it.
In "Rising Tides, Crashing Skies", he appears at his desk being interviewed by Ronaldo being asked about the Gem Warship, but he confuses it for people voting to save Beach City by electing, but he soon finds out that he's talking about the Crystal Gems. He asks why he's talking about them, and Ronaldo says he's covering the story about them, but he then confuses it for asking about a cover-up and gets security to eject him from his office.