  We present new measurements of the oxygen gas-phase abundance along four
sightlines probing gas inside the Local Bubble, using data obtained with the
Far Ultraviolet Spectroscopic Explorer (FUSE) and the Hubble Space Telecope
(HST). Combining these with seven previously published N(O I) and N(H I)
measurements we determine a mean O/H ratio for the Local Bubble, (O/H) = (3.45
+/- 0.19)x10^(-4) (1 sigma in the mean). Our result is virtually identical to
O/H = (3.43 +/- 0.15)x10^(-4) derived from data for sightlines probing gas well
outside the Local Bubble. In contrast to the D/O and D/H ratios, which seem to
have different values beyond the Local Bubble, our results show that the O/H
ratio is constant and single-valued both inside and outside the Local Bubble,
for low density sightlines, with column densities up to log N (H) ~ 21. In
addition, the similarity of the two values above suggests that the net effect
of the uncertain O I f-values in the FUSE bandpass is not significant. Taking
into account the latest determinations of the Solar abundance of oxygen, our
result implies that ~25% of the oxygen in the Local Bubble is depleted onto
dust grains. The similarity of the value for O/H along low average density
sightlines in the Local Bubble with that of denser sightlines beyond may permit
a limit on the diluting effects of infalling low metallicity gas.
