  Recent high-resolution angle-resolved photoemission spectroscopy experiments
have given a reason to believe that pure bismuth is topologically non-trivial
semimetal. We derive an analytic theory of surface and size-quantized states of
Dirac fermions in Bi(111) films taking into account the new data. The theory
relies on a new phenomenological momentum-dependent boundary condition for the
effective Dirac equation. The boundary condition is described by two real
parameters that are expressed by a linear combination of the Dresselhaus and
Rashba interface spin-orbit interaction parameters. In semi-infinite Bi(111),
near $\overline{\rm M}$-point the surface states possess anisotropical
parabolic dispersion with very heavy effective mass in $\overline{\rm
\Gamma}-\overline{\rm M}$ direction order of ten free electron masses, and
light effective mass in $\overline{\rm M}-\overline{\rm K}$ direction order of
one hundredth of free electron mass. In Bi(111) films with equivalent surfaces,
the surface states from top and bottom surfaces are not splitted. In such
symmetric film with arbitrary thickness, bottom of the lowest quantum
confinement subband in conduction band coincides with the bottom of bulk
conduction band in $\overline{\rm M}$-point.
