A bowler hat was type of hat.
Whilst visiting Victorian England to look into "the Crimson Horror", the Eleventh Doctor wore a bowler hat. (TV: The Crimson Horror)
The Fourth Doctor briefly wore a bowler hat he found in Fang Rock lighthouse whilst investigating it. (TV: Horror of Fang Rock)
In the 1970s, a Time Lord messenger dressed as an English businessman, complete with bowler hat and umbrella, appeared to the Third Doctor to warn him that the Master was on Earth. (TV: Terror of the Autons)
The Eighth Doctor wore a bowler hat. (PROSE: Endgame)
On Earth, the Council of Dead wore identical pin-stripe suits and bowler hats to cover their horns. (PROSE: Snowfall, Attack of the Snowmen)
Hargreaves wore a black bowler hat while in his butler form. (AUDIO: Aquitaine)
The Tremas Master wore a bowler hat while on a train taunting the Graak. (GAME: Destiny of the Doctors)
Graham O'Brien wore a bowler hat during a trip to New York during 1903. (TV: Nikola Tesla's Night of Terror).
One version of the Corsair wore a black bowler hat. (PROSE: Eleven Things You Probably Didn't Know About the Corsair)