We report the control of the modulation efficiency of the magnon conductivity in yttrium iron garnet (YIG) using magnon spin injection from a ferromagnetic metal permalloy (Py) used as a modulator in a three-terminal magnon transistor geometry. The modulation efficiency is estimated by means of nonlocal spin-transport measurements between platinum injector and detector strips. A charge current is sent through the Py modulator to create a spin accumulation at the YIG-Py interface via the spin Hall effect and the anomalous spin Hall effect (ASHE). We observe an enhancement of the modulation efficiency for the electrically generated magnons from 2.5%/mA at 10 mT to 4.7%/mA for magnetic fields higher than 50 mT. That enhancement is attributed to the ASHE, which is maximized when the Py magnetization is perpendicular to the charge current. However, the modulation efficiency of the thermally generated magnons exhibits an opposite behavior, 12.0%/mA at 10 mT to 6.6%/mA at 50 mT, which disagrees with what we expect from the ASHE contribution to the modulation.