Spin dynamics of field-driven domain walls (DWs) guided by permalloy nanowires are studied by high-speed magneto-optic polarimetry and numerical simulations. DW velocities and spin configurations are determined as functions of longitudinal drive field, transverse bias field, and nanowire width. Nanowires having cross-sectional dimensions large enough to support vortex wall structures exhibit regions of drive-field strength (at zero bias field) that have enhanced DW velocity resulting from coupled vortex structures that suppress oscillatory motion. Factor of 10 enhancements of the DW velocity are observed above the critical longitudinal drive-field (that marks the onset of oscillatory DW motion) when a transverse bias field is applied. Nanowires having smaller cross-sectional dimensions that support transverse wall structures also exhibit a region of higher mobility above the critical field, and similar transverse-field induced velocity enhancement but with a smaller enhancement factor. The bias-field enhancement of DW velocity is explained by numerical simulations of the spin distribution and dynamics within the propagating DW that reveal dynamic stabilization of coupled vortex structures and suppression of oscillatory motion in the nanowire conduit resulting in uniform DW motion at high speed. The enhanced velocity and drive field range are achieved at the expense of a less compact DW spin distribution.