Spatially structured electromagnetic fields such as surface plasmon polaritons (SPPs) possess transverse spin angular momentum (t-SAM) in the direction perpendicular to the axis of propagation. In this work, we numerical calculated the SAM distribution of the space-time surface plasmon polariton (ST-SPP) wave packet (WP), a plasmonic bullet that propagates at an arbitrary group velocity while maintaining its spatial distribution. The out-of-plane component of the t-SAM which appear at the center of the ST-SPP WP is framed by L-lines that forms a series of split rings. The distribution of the t-SAM and the L-line maintains even after the WP propagation more than twice the SPP attenuation length. This suggests the ST-SPP WP can provide robust and group-velocity tunable transportations of three-dimensional spin textures on material surfaces.