  We have studied the reaction $ep \to ep \gamma$ in the kinematics
corresponding to electron scattering at small angles and photon scattering at
large angles, where proton bremsstrahlung dominates. The analysis is based on
the direct evaluation method of the matrix elements in the so-called diagonal
spin basis. The results of numerical calculations for electron beam energy
$E_{e}=200 MeV$ in the above kinematics show that the relative contribution of
the Bethe-Heitler and interference terms to the reaction cross section is less
than 10 %, and the cross section for the reaction $ep \to ep \gamma$ is quite
sensitive to the proton polarizability. Owing to the factorization of the
squared electric and magnetic form factors of the proton, a compact expression
has been obtained for the differential cross section of the Bethe-Heitler
emission of a linearly polarized photon by an electron, taking into account the
proton recoil and form factors. A covariant expression has been obtained for
the lepton tensor in which contributions of states with transverse and
longitudinal polarizations of the virtual photon are separated.
