Bud really is an awful name for a tropical cyclone. I'm guessing that was an American-proposed name, I can't see Mexico suggesting that.
"Bud" has been on the name list since they added male names. It was used for the first time in 1982 and has been used every single time it has come up, making appearances in 1988, 1994, 2000, and 2006 as well. It has only reached Hurricane status once, in 2000, and has never made landfall, though the 1988 Tropical Storm Bud did hug the coastline and dump a lot of rain on parts of southwest Mexico.