  We study new solutions of black bounce spacetimes formulated in $f(T)$
gravity in four dimensions. First, we present the case of a diagonal tetrad,
where a constraint arises in the equations of motion, which is divided into the
cases of null torsion, constant torsion, and Teleparallel. The Null Energy
Condition (NEC) is still always violated, which implies that the other energy
conditions are violated. The solutions are regular in all spacetime and the
solution with null torsion exhibits discontinuity between the energy conditions
outside and inside the event horizon. Second, we present the case of
non-diagonal tetrads. This case is divided into a Simpson-Visser type model and
a quadratic model. The NEC continues to be violated, implying a violation of
the other energy conditions. The solutions are regular in all spacetimes. An
interesting result is that due to the possibility that the area associated with
the metric is different from $4\pi r^2$, the no-go theorem established in the
usual $f(T)$ is violated, appearing the new possibility $g_{00}=-g^{11}$, for
the components of the metric.
