We report measurements of Shubnikov-de Haas oscillations in single crystals of BiTeCl at magnetic fields up to 31 T and at temperatures as low as 0.4 K. Two oscillation frequencies were resolved at the lowest temperatures, F-1 = 65 +/- 4 T and F-2 = 156 +/- 5 T. We also measured the infrared optical reflectance [R(omega)] and Hall effect; we propose that the two frequencies correspond respectively to the inner and outer Fermi sheets of the Rashba spin-split bulk conduction band. The bulk carrier concentration was n(e) approximate to 1 x 10(19) cm(-3) and the effective masses m(1)* = 0.20m(0) for the inner and m(2)* = 0.27m(0) for the outer sheet. Surprisingly, despite its low effective mass, we found that the amplitude of F-2 is very rapidly suppressed with increasing temperature, being almost undetectable above T approximate to 4 K.