  We consider a fully pseudo-bosonic Swanson model and we show how its
Hamiltonian $H$ can be diagonalized. We also deduce the eigensystem of
$H^\dagger$, using the general framework and results deduced in the context of
pseudo-bosons. We also construct, using different approaches, the bi-coherent
states for the model, study some of their properties, and compare the various
constructions.
