The chronology of bulge and disk formation is a major unsolved issue in galaxy formation, which impacts on our global understanding of the Hubble sequence. We present colours of the nuclear regions of intermediate-redshift disk galaxies, with the aim of obtaining empirical information of ages of bulges at intermediate z. We work with a sample of 248 galaxies (123 inclined + 125 face-on) from the HST Groth Strip Survey (Groth et al. 1994) and another one with 404 objects (214 inclined + 190 face-on) from the HST GOODS-N field (Giavalisco et al. 2004), covering redshifts 0.1 < z < 1.3. Those samples are apparent-diameter limited at R > 1.4″. We find that, as in the Local Universe, the minor axis color profiles are negative (bluer outward), and fairly gentle, indicating that bulge colours are not distinctly different from disk colours. We apply a conservative criterion to identify bulges and potential precursors of present-day bulges, based on nuclear excess surface brightness above the exponential profile of the outer parts. For galaxies with central brightness excesses, rest-frame colour distributions show a red sequence that confirms the finding of very red bulges by Koo et al. (2005), using independent methods. In contrast, galaxies without central brightness excesses show typical colours of star-forming populations. Clearly, something had truncated star formation in many high-density cores, already at z ~ 1. The truncation epoch is uncertain, 1.5 < z < 10. The colour-magnitude distribution of intermediate-z bulges shows more colour dispersion than that of bulges in the Local Universe. About 50% of bulges are as red as local bulges, while the remainder are significantly bluer, a possible sign of late bulge formation. We also find that bulge colours correlate with integrated galaxy colours and with their disk colours.