The asymmetric background conductance linear in bias voltage usually observed in Bal "KBi03 superconductor-insulator-normal (SIN) tunnel junctions is associated with a zero-bias conductance linear in temperature above the superconducting transition. The ratio of the temperature coefficient and the voltage coefficient provides insight into the mechanism causing the linear background conductance.We present a simple model involving tunnehng through two-particle states (negative-U, bipolaron) in the barrier that explains the linear background, the asymmetry, and the linear temperature dependence of the conductance. Measurements of native-barrier Bal K Bi03 tunnel junctions are in quantitative agreement with the model. Since its discovery, Ba, K"Bi03 (0.4 (x (Q.5) (BKBO) (Refs. 1 and 2) has been considered a useful point of comparison to the high-T, cuprate superconductors. Unlike the cuprates, BKBO and its close relatives, Ba, "RbBi03 and BaPb, Bi O3, are known to have a clean gap in tunneling with 2A/kz T, =3. 5, consistent with weak-to-moderate coupling BCS theory. From the isotope shift, inelastic neutron scattering, ' tunneling spectra, ' '" and the normal-state properties, ' it is generally accepted that electron-phonon coupling plays at least a partial role in the superconductivity. The cubic structure and lack of magnetic ions further simplify the theory of superconductivity in BKBO. On the other hand, the high-T, (up to 31 K), especially given the low electronic density of states N*, suggests that a deeper physical understanding of BKBO will be relevant to understanding other high-T, materials. Particularly intriguing are the analogous electronic phase diagrams in the cuprate and bismuthate systems. High-temperature superconducting states in both systems are proximate to collective-mode insulator states (the charge-density-wave semiconductor in BaBi03 and the antiferromagnetic insulator in the cuprates). A disordered or glassy state, characterized by variable-range-hopping conductivity, ' lies in between.Perhaps the most striking similarly between the bismuthate and cuprate superconductors is the asymmetric linear background conductance seen in tunnel junctions. ' Even though the linear background has been most widely discussed in the context of YBa2Cu307 etched-surface junctions, BizSr2CaCu208 cleaved surface junctions, and Bi2Sr2CaCu208 point-contact junctions, the phenomenon appears to be even more robust in the bismuthate systems. The apparent differences between tunneling perpendicular to and along copper oxygen planes have led to explanations for the linear background conductance that depend on the strong anisotropy of the cuprates, thus ignoring the similar phenomena in the cubic bismuthates. There are several important differences between the linear backgrounds in cuprate junctions and in bismuthate junctions. One is the sign of the asymmetry: in bismuthate junctions, the conductance is always higher with the metal electrode negatively biased, while for cuprates, the conductance is always higher wit...