We have obtained high resolution Echelle spectra ( R = 30,000 - 50,000 ) of the Na D absorption doublet ( \lambda \lambda 5890 , 5896 ) for six dwarf starburst galaxies and two more luminous starbursts : M82 and NGC 1614 . The absorption features were separated into multiple components and separated into stellar and interstellar parts based on kinematics . We find that three of the dwarfs show outflows , with an average blueshift of 27 km s ^ { -1 } . This is small compared to the highest velocity components in NGC 1614 and M82 ( blueshifted by 150 km s ^ { -1 } and 91 km s ^ { -1 } , respectively ) ; these two brighter galaxies also show more complex absorption profiles than the dwarfs . None of the outflow speeds clearly exceed the escape velocity of the host galaxy . Sightlines in NGC 2363 and NGC4214 apparently intersect expanding shells . We compare the shocked gas velocity ( v _ { NaD } ) to the ionized gas velocity ( v _ { H \alpha } ) and interpret the velocity difference as either a trapped ionization front ( NGC 4214 ) or a leaky H ii region ( NGC 2363 ) . The dwarfs show N _ { NaD } = 10 ^ { 11.8 - 13.7 } cm ^ { -2 } , while the Na D columns in M82 and NGC 1614 are 10 ^ { 13.7 } cm ^ { -2 } and 10 ^ { 14.0 } cm ^ { -2 } , respectively . The mass of expelled gas is highly sensitive to outflow geometry , dust depletion , and ionization fraction , but with a simple shell model we estimate neutral outflow gas masses from \sim 10 ^ { 6 } M _ { \odot } to \sim 10 ^ { 10 } M _ { \odot } .