Experiments on the Hall coefficient R_H and heat capactity C reveal an unusual, compensated electronic ground state in the ruthenate Bi_3Ru_3O_11. At low temperature T, R_H decreases linearly with magnetic field |H| for fields larger than the field scale set by the Zeeman energy. The results suggest that the electron and hole populations are tuned by H in opposite directions via coupling of the spins to the field. As T is decreased below 5 K, the curve C(T)/T vs. T^2 shows an anomalous flattening consistent with a rapidly growing Sommerfeld parameter γ(T). We discuss shifts of the electron and hole chemical potentials by H to interpret the observed behavior of R_H. ; Comment: 5 pages, 6 figures, reference added