  We describe medium-resolution spectroscopic observations taken with the ESO
Multi-Mode Instrument in the CaII K line (3933.661 Angstroms) towards 7 QSOs
located in the line-of-sight to the Magellanic Bridge. At a spectral resolution
R = 6,000, five of the sightlines have a signal-to-noise ratio of 20 or higher.
Definite Ca absorption due to Bridge material is detected towards 3 objects,
with probable detection towards two other sightlines. Gas-phase CaII K Bridge
and Milky Way abundances or lower limits for the all sightlines are estimated
by the use of Parkes 21-cm HI 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 CaII K detections, we find that the ionic abundance of CaII K
relative to HI, A=log(N(CaK)/N(HI)) for low-velocity Galactic gas ranges from
-8.3 to -8.8 dex, with HI column densities varying from 3-6x10^20 cm^-2. For
Magellanic Bridge gas, the values of A are 0.5 dex higher, ranging from -7.8 to
-8.2 dex, with N(HI)=1-5x10^20 cm^-2. Higher values of A correspond to lower
values of N(HI), although numbers are small. For the sightline towards
B0251--675, the Bridge gas has two different velocities, and in only one of
these is CaII K 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 CaII K data
and higher resolution HI data are required to determine whether A changes with
N(HI) over the Bridge and if the implied difference in the metalicity of the
two Bridge components towards B0251-675 is real.
