Electrical conduction and relaxation phenomena in bismuth borate glasses in the composition 2Bi2O3–B2O3 (Bi4B2O9) were investigated. Dielectric studies carried out on these glasses revealed near constant loss response in the 1 kHz–1 MHz frequency range at moderately high temperatures (300–450 K) associated with relatively low loss (tan δ = 0.006) and high dielectric constant (εr′ = 37) at 1 kHz, 300 K. The variation in AC conductivity with temperature at different frequencies showed a cross over from near constant loss response characterized by local ion vibration within the potential well to universal Jonscher's power law dependence triggered by ion hopping between potential wells or cages. Thermal activation energy for single potential well was found to be 0.48 ± 0.05 eV from cross over points. Ionic conduction and relaxation processes were rationalized by modulus formalism. The promising dielectric properties (relatively high εr′ and low tan δ) of the present glasses were attributed to high density (93% of its crystalline counterpart), high polarizability, and low mobility associated with heavy metal cations, Bi3+.