Motivated by the possibility of exploiting species containing high spin quantum number nuclei (referred to as quadrupole nuclei) as novel contrast agents for Magnetic Resonance Imaging, based on Quadrupole Relaxation Enhancement (QRE) effects, 1H spin-lattice relaxation has been investigated for tris(2-methoxyphenyl)bismuthane and tris(2,6-dimethoxyphenyl)bismuthane in powder. The relaxation experiment has been performed in the magnetic field range of 0.5 T to 3 T (the upper limit corresponds to the field used in many medical scanners). A very rich QRE pattern (several frequency specific 1H spin-lattice relaxation rate maxima) has been observed for both compounds. Complementary Nuclear Quadrupole Resonance experiments have been performed in order to determine the quadrupole parameters (quadrupole coupling constant and asymmetry parameters) for 209Bi. Knowing the parameters, the QRE pattern has been explained on the basis of a quantum-mechanical picture of the system including single and double-quantum coherences for the participating nuclei (1H and 209Bi). In this way the quantum-mechanical origin of the spin transitions leading to the QRE effects has been explained.