We experimentally demonstrate bidirectional Raman soliton-like combs in a whispering gallery mode microresonator with a unidirectional pump for the first time, to the best of our knowledge. We develop a relatively simple theoretical model and find an analytical solution for forward- and backward-propagating Raman sech2-shaped solitons in an anomalous dispersion region under unidirectional pumping in a normal dispersion region. Raman solitons exist, thanks to the balance between losses and Raman gain from a CW wave (which is equal in both directions) as well as between dispersion and Kerr nonlinearity.