The infrared reflectivity of single crystals of ${\mathrm{Bi}}_{2}$${\mathit{M}}_{\mathit{m}+1}$${\mathrm{Co}}_{\mathit{m}}$${\mathrm{O}}_{\mathit{y}}$ (M=Ca, Sr, Ba; m=1,2), ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{3}$${\mathrm{Fe}}_{2}$${\mathrm{O}}_{9.2}$, and ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{MnO}}_{6.25}$ was measured at room temperature between 0.08 and 1.4 eV. A broad absorption band is observed in the mid-ir range (near 0.5 eV) in all the compounds studied, and an absorption band near 0.3 eV is observed in the insulating system. In terms of a conventional Drude-Lorentz model, the measured reflectivity and the frequency-dependent conductivity between 0.2 and 1 eV can be fitted with three broad Lorentzians and a Drude term. For the ${\mathrm{Bi}}_{2}$${\mathit{M}}_{\mathit{m}+1}$${\mathrm{Co}}_{\mathit{m}}$${\mathrm{O}}_{\mathit{y}}$ system, the reflectivity increases and assumes a more metallic profile as the number of Co-O layers per unit cell increases, or as the ionic radius of M increases. The apparent plasma edge of this system is about 0.3 eV, and remains unshifted for all ${\mathrm{Bi}}_{2}$${\mathit{M}}_{3}$${\mathrm{Co}}_{2}$${\mathrm{O}}_{\mathit{y}}$, as observed in the high-${\mathit{T}}_{\mathit{c}}$ cuprates in which the carrier density is changed by doping. In addition, as observed in the high-${\mathit{T}}_{\mathit{c}}$ cuprates, the reflectivity-frequency profile below the apparent plasma edge is less curved than predicted by the Drude model. For the ${\mathrm{Bi}}_{2}$${\mathit{M}}_{\mathit{m}+1}$${\mathrm{Co}}_{\mathit{m}}$${\mathrm{O}}_{\mathit{y}}$ system, the intensity of the mid-ir absorption approximately scales with that of the free-carrierlike absorption.The compounds ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{3}$${\mathrm{Fe}}_{2}$${\mathrm{O}}_{9.2}$ and ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{MnO}}_{6.25}$ appear more insulating in reflectivity measurements than does ${\mathrm{Bi}}_{2}$${\mathit{M}}_{\mathit{m}+1}$${\mathrm{Co}}_{\mathit{m}}$${\mathrm{O}}_{\mathit{y}}$. However, the intensity of the mid-ir absorption in these crystals is slightly larger. Our results suggest that the existence of a mid-ir absorption band is not a sufficient condition for the occurrence of high-${\mathit{T}}_{\mathit{c}}$ superconductivity.