Hot-film anemometry measurements are performed in a fully developed turbulent bubbly flow. For the bubble detection in the signal, both a threshold method and a new pattern recognition algorithm are employed. The measurements are carried out with gas fractions up to 3% and a mean water velocity of 0.20 m s$^{-1}$, corresponding to a Reynolds number of about $9\,{\times}\,10^4$. The typical bubble radius is 1–2 mm, corresponding to 10–20 Kolmogorov length scales. In this regime, a ‘bubblance’ parameter $b$ which compares the kinetic energy originating from the rising bubbles with that of the turbulence fluctuations is smaller than 1. Probability distribution functions, structure functions (with and without the extended self-similarity (ESS) method), and spectra of the water velocity time series are calculated. Both our results for the turbulent energy spectra and the second-order structure functions show qualitative agreement with numerical results by Massitelli, Lohse & Toschi (Phys. Fluids, vol. 15 (2003), p. L5), i.e. a more pronounced energy enhancement on small scales than on large scales owing to the presence of bubbles, leading to a less steep slope in the spectrum as compared to the Kolmogorov $-5/3$ law. These results are robust, i.e. do not depend on details of the bubble detection scheme.