Context. Determining elemental abundances of bulge stars can, via chemical evolution modeling, help to understand the formation and evolution of the bulge. Recently there have been claims both for and against the bulge having a different [alpha/Fe] versus [Fe/H] trend as compared to the local thick disk. This could possibly indicate a faster, or at least different, formation timescale of the bulge as compared to the local thick disk. Aims. We aim to determine the abundances of oxygen, magnesium, calcium, and titanium in a sample of 46 bulge K giants, 35 of which have been analyzed for oxygen and magnesium in previous works, and compare this sample to homogeneously determined elemental abundances of a local disk sample of 291 K giants. Methods. We used spectral synthesis to determine both the stellar parameters and elemental abundances of the bulge stars analyzed here. We used the exact same method that we used to analyze the comparison sample of 291 local K giants in Paper I of this series. Results. Compared to the previous analysis of the 35 stars in our sample, we find lower [Mg/Fe] for [Fe/H] > -0.5, and therefore contradict the conclusion about a declining [O/Mg] for increasing [Fe/H]. We instead see a constant [O/Mg] over all the observed [Fe/H] in the bulge. Furthermore, we find no evidence for a different behavior of the alpha-iron trends in the bulge as compared to the local thick disk from our two samples.