  The present paper is devoted to a new black bounce solution that regularize
the well-known rotating black string in $3+1$ dimensions. To do so, the
procedure pointed out by Simpson-Visser is followed, which has been already
applied successfully to other static cases of black strings, with and without
electric charge. This method implies to force a bounce on the radial
coordinate, such that a wormhole throat arises before the singularity, which
renders a regular solution. An analysis of the metric is conducted, showing the
interpolation between a regular black hole and a wormhole, what provides a much
richer family of solutions than the original metric. Different curvature
magnitudes are obtained in order to analyze the regularity of the solution,
including the Ricci and Kretschmann scalars. Finally, by following the Einstein
field equations the corresponding effective energy-momentum tensor is obtained
and the energy conditions are analyzed.
