Context. Technetium (Tc) is an unstable element synthesised via the s-process in deep layers of asymptotic giant branch (AGB) stars, making it a reliable indicator of both recent s-process activity and third dredge-up. Aims. We searched for Tc in a sample of bright oxygen-rich asymptotic giant branch (AGB) stars located in the outer galactic bulge. We test theoretical predictions of the luminosity limit for the onset of third dredge-up. Methods. Using high-resolution optical spectra obtained with the UVES spectrograph at ESO's VLT, we searched for resonance lines of neutral Tc in the blue spectral region of our sample stars. These measurements allow us to improve the procedure of classification of stars with respect to their Tc content by using flux ratios. Synthetic spectra based on MARCS atmospheric models are presented and compared to the observed spectra around three lines of Tc. Bolometric magnitudes are calculated based on the near-infrared photometry of the objects. Results. Among the sample of 27 long-period bulge variables, four were found to definitely contain Tc in their atmospheres. The luminosity of the Tc-rich stars agrees with predictions from AGB evolutionary models on the minimum luminosity at the time when third dredge-up sets in. However, AGB evolutionary models and a bulge consisting of a single old population cannot be brought into agreement. This probably means that a younger population is present in the bulge, as suggested by various authors, that contains the Tc-rich stars identified here.