From the Super Mario Wiki
Bud is a fictional Real World boy who makes one appearance in the episode "Mush-Rumors" in the TV series, The Adventures of Super Mario Bros. 3. He is the son of Norman, whom is driving his family, Missy and Bud and Missy's mother to an amusement park, called Wild Waldo's One-of-a-Kind Amusement Park. The family accidentally drives into a Warp Zone, which leads them to the Mushroom World.
When Norman says that the scenery turned weird, Bud exclaims that it is cool, while Missy exclaims that it is freaky. After Norman drives into a wall of Blocks, Bud sarcastically remarks, "Nice going Dad." Norman then crashes into another wall of Blocks, which nearly totals the car. This causes tension in a Mushroomer, who witnessed the entire event, and goes screaming off to the Mushroom World that the "aliens" have arrived.
Right before Mario and Luigi inspect the crash, Bud suggests that they are in Wild Waldo's One-of-a-Kind Amusement Park. Mario and Luigi then save the family from the Doomship by throwing the car on an inflatable raft. After the Doomship starts firing Bullet Bills and Bob-ombs, Bud remarks, "This is the best amusement park we have ever been to." Mario and Luigi then protect the station wagon, but the Doomship afterward takes the station wagon by a magnet.
While the rest of the family is frightened by King Koopa inside his castle, Bud remarks by asking what is going on and that the green geezer is very "bizotic." Kooky von Koopa then uses his Transmutational Brainwave Analyzer in his lab on the family. The Mario Bros. then rescue the family and sends them home via Warp Zone.