We have investigated the thermal, electrical, and structural properties of Bi and BiCu films that are being developed as X-ray absorbers for transition-edge sensor (TES) microcalorimeter arrays for imaging X-ray spectroscopy. Bi could be an ideal material for an X-ray absorber due to its high X-ray stopping power and low specific heat capacity, but it has a low thermal conductivity, which can result in position dependence of the pulses in the absorber. In order to improve the thermal conductivity, we added Cu layers in between the Bi layers. We measured electrical and thermal conductivities of the films around 0.1 K, the operating temperature of the TES calorimeter, to examine the films and to determine the optimal thickness of the Cu layer. From the electrical conductivity measurements, we found that the Cu is more resistive on the Bi than on a Si substrate. Together with a SEM picture of the Bi surface, we concluded that the rough surface of the Bi film makes the Cu layer resistive when the Cu layer is not thick enough to fill in the roughness. From the thermal conductivity measurements, we determined the thermal diffusion constant to be 2 x 103 μm2μs-1 in a film that consists of 2.25 μm of Bi and 0.1 μm of Cu. We measured the position dependence in the film and found that its thermal diffusion constant is too low to get good energy resolution, because of the resistive Cu layer and/or possibly a very high heat capacity of our Bi films. We show plans to improve the thermal diffusion constant in our BiCu absorber.