  We propose a method to exactly generate bridge run-and-tumble trajectories
that are constrained to start at the origin with a given velocity and to return
to the origin after a fixed time with another given velocity. The method
extends the concept of effective Langevin equations, valid for Markovian
stochastic processes such as Brownian motion, to a non-Markovian stochastic
process driven by a telegraphic noise, with exponentially decaying
correlations. We obtain effective space-time dependent tumbling rates that
implicitly accounts for the bridge constraint. We extend the method to other
types of constrained run-and-tumble particles such as excursions and meanders.
The method is implemented numerically and is shown to be very efficient.
