He will still buck (usually) until the strap is loosened, just not nearly as vigorously. While you’re watching to see if the bull is going to stomp/gore/otherwise injure the rider who just got bucked off, one of the clowns or the pickup rider on horseback is busy trying to release the flanking strap. The bull rope that the rider uses to hold on with comes loose by itself with the rider dismounts (voluntarily or otherwise).
Have any of you seen “Bull Pinball” or “Cowboy Pinball” ?
https://www.youtube.com/watch?v=A7NMGO7Pb0o