This would mean that something was very funny. The image is of you laughing so hard your sides burst open. It's an exaggeration.
Well, darling, a sidebuster is slang for a person who is an outsider or an uninvited guest at a social gathering. So, if you find yourself crashing a party or sticking your nose where it doesn't belong, you might just be labeled as a sidebuster. Just remember, it's always better to be the life of the party than the one everyone wishes would just bust on out of there.
Well, honey, cowboys called people "sidebusters" because they were greenhorn newcomers who rode on the side of the trail and didn't know what the heck they were doing. It's like calling someone a rookie or a clueless tagalong. So, if you find yourself being called a sidebuster, just embrace it and learn from those seasoned cowboys.