From the Super Mario Wiki
The Bowser Suit (sometimes Bowser Mushroom in Mario Party 4) is a somewhat rare item that first appears in Mario Party 2. When used, the character who used it will wear a Bowser costume and be able to take twenty coins from every opponent he or she passes during their roll. A Koopa Kid may even give a character dressed in a Bowser Suit coins as well.
In Mario Party 3, Bowser Suits can sometimes be purchased from Baby Bowser at the Item Shops.
In Mario Party 4, players can only acquire a Bowser Suit by landing on a Bowser Space and even then, the chances of getting one are slim to none. Waluigi is even pictured holding it on the box art of Mario Party 4. In that game it strongly resembles a Mushroom, giving it the nickname Bowser Mushroom. A player using the Bowser Suit can steal 30 coins from passing an opponent. Additionally, if a player wearing the suit passes Bowser on Bowser's Gnarly Party, they will get 50 coins.
The Bowser Suit's equivalent in Mario Party 5 and Mario Party 6 is the Bullet Bill Capsule.
The Bowser Suit reappears in Mario Party 8 when a player uses the Bowser Candy, this time letting the character to hit two dice and being able to steal two Stars from everyone the player passes. It only appears in Bowser's Warped Orbit.
In addition, the Bowser Suit is used in the original Mario Party game in some 1-vs-3 minigames such as Bash 'n' Cash and Tug o' War.