We present 21cm HI line observations of the blue compact dwarf galaxy NGC1705. Previous optical observations show a strong outflow powered by an ongoing starburst dominating the HII morphology and kinematics. In contrast, most of the HI lies in a rotating disk. An extraplanar HI spur accounts for ~ 8% of the total HI mass, and is possibly associated with the HII outflow. The inferred mass loss rate out of the galaxys core is significant ~ 0.2 - 2 M_sun/yr, but does not dominate the HI dynamics. Mass model fits to the rotation curve show that the dark matter (DM) halo is dominant at nearly all radii and has a central density rho_0 approx 0.1 M_sun/pc^3: ten times higher than typically found in dwarf irregular galaxies, but similar to the only other mass-modelled blue compact dwarf, NGC2915. This large difference strongly indicates that there is little evolution between dwarf irregular and blue compact dwarf types. Instead, dominant DM halos may regulate the morphology of dwarf galaxies by setting the critical surface density for disk star formation. Neither our data nor catalogue searches reveal any likely external trigger to the starburst in NGC1705.