We present a series of measurements on various aspects of cyclotron resonance in Bi at far-infrared laser frequencies (890.7, 964.3, 1539.5, and 2526.6 GHz). The experiments make use of a spectrometer where the sample forms one plate of a TEM-mode strip transmission line. We observe subharmonics of cyclotron resonance which appear split into a number of distinct resonance lines, each due to a particular transition between Landau levels of the nonparabolic conduction band of Bi. From the line positions for the binary-axis low-mass resonance we determine the band parameters ${E}_{g}=13.0\ifmmode\pm\else\textpm\fi{}2$ meV and $m_{}^{*}{}_{c}{}^{}=(0.00170\ifmmode\pm\else\textpm\fi{}0.00025){m}_{0}$. The temperature dependence of the amplitudes of the resonance lines gives ${E}_{F}=29.7\ifmmode\pm\else\textpm\fi{}0.5$ meV. We observe the amplitude decay of successive subharmonics of the resonance and show that the amplitude decreases with subharmonic number $n$ approximately as ${(\frac{R}{\ensuremath{\delta}})}^{2n\ensuremath{-}2}$ for the binary-axis signal. In addition to cyclotron resonance, we observe and identify various impedance anomalies as due to cyclotron-wave propagation. Finally, we present some evidence for an energy-dependent relaxation time in Bi, from the observation that cyclotron-resonance linewidths are related to the energy separation of Landau level and Fermi energy.