A data storage device is disclosed comprising a head actuated over a disk, wherein the head comprises a spin torque oscillator (STO). A first bias signal is applied to the STO during a first interval preceding a write operation to write data to the disk, wherein the first bias signal causes the STO to protrude toward the disk. After the first interval, a second bias signal is applied to the STO during a second interval spanning at least part of the write operation, wherein an amplitude of the first bias signal is in the range of 1.1 to 1.5 times an amplitude of the second bias signal.