The excitation function for production of 262Bh in the odd-Z-projectile reaction 208Pb(55Mn,n) has been measured at three projectile energies using the Berkeley Gas-filled Separator at the Lawrence Berkeley National Laboratory 88-Inch Cyclotron. In total, 33 decay chains originating from 262Bh and 2 decay chains originating from 261Bh were observed. The measured decay properties are in good agreement with previous reports. The maximum cross section of 540 +180 -150 pb is observed at a lab-frame center-of-target energy of 264.0 MeV and is more than fives times larger than that expected based on previously reported results for production of 262Bh in the analogous even-Z-projectile reaction 209Bi(54Cr,n). Our results indicate that the optimum beam energy in one-neutron-out heavy-ion fusion reactions can be estimated simply using the "Optimum Energy Rule" proposed by Swiatecki, Siwek-Wilczynska, and Wilczynski.