It's Bully Wee and the origin is unknown although there are three theories;
The club's nickname, "The Bully Wee", is of uncertain origin although the club themselves have advanced three theories.
The first suggests that the clubs and supporters and perhaps players mainly came from Bridgeton, Glasgow, a tight working-class area whose inhabitants had a reputation as "wee bullies", with this becoming transposed as the Bully Wee.
Alternatively, it is also claimed that it comes from around 1900 when a group of French supporters paid a visit to Barrowfield and, upon the scoring of a disputed goal, were heard to remark "But il'y, oui?" or "Their goal, yes". Supporters listened to this unfamiliar phrase as "Bully Wee", and the name stuck.
Finally the third theory, and the one accepted by the club as the most plausible, links the term to the old Victorian idiom "bully" meaning first-rate or high standard and suggests that Clyde, a small club, would have been regularly referred to as "Bully Wee Clyde", with the first two words eventually becoming the standalone nickname.