We describe medium-resolution spectroscopic observations taken with the ESO Multi-Mode Instrument ( emmi ) in the Ca ii K line ( \lambda _ { air } =3933.661Å ) towards 7 QSOs located in the line-of-sight to the Magellanic Bridge . At a spectral resolution R = \lambda / \Delta \lambda = 6,000 , five of the sightlines have a signal-to-noise ( S/N ) ratio of \sim 20 or higher . Definite Ca absorption due to Bridge material is detected towards 3 objects , with probable detection towards two other sightlines . Gas-phase Ca ii K Bridge and Milky Way abundances or lower limits for the all sightlines are estimated by the use of Parkes 21-cm H i emission line data . These data only have a spatial resolution of 14 arcminutes compared with the optical observations which have milli-arcsecond resolution . With this caveat , for the three objects with sound Ca ii K detections , we find that the ionic abundance of Ca ii K relative to H i , A =log ( N ( Ca K ) / N ( H i ) ) for low-velocity Galactic gas ranges from –8.3 to –8.8 dex , with H i column densities varying from 3 - 6 \times 10 ^ { 20 } cm ^ { -2 } . For Magellanic Bridge gas , the values of A are \sim 0.5 dex higher , ranging from \sim –7.8 to –8.2 dex , with N ( H i ) =1–5 \times 10 ^ { 20 } cm ^ { -2 } . Higher values of A correspond to lower values of N ( H i ) , although numbers are small . For the sightline towards B 0251–675 , the Bridge gas has two different velocities , and in only one of these is Ca ii tentatively detected , perhaps indicating gas of a different origin or present-day characteristics ( such as dust content ) , although this conclusion is uncertain and there is the possibility that one of the components could be related to the Magellanic Stream . Higher signal-to-noise Ca ii K data and higher resolution H i data are required to determine whether A changes with N ( H i ) over the Bridge and if the implied difference in the metalicity of the two Bridge components towards B 0251-675 is real .