As part of the international Matroshka-R and Radi-N experiments, bubble detectors have been used on board the ISS in order to characterise the neutron dose and the energy spectrum of neutrons. Experiments using bubble dosemeters inside a tissue-equivalent phantom were performed during the ISS-16, ISS-18 and ISS-19 expeditions. During the ISS-20 and ISS-21 missions, the bubble dosemeters were supplemented by a bubble-detector spectrometer, a set of six detectors that was used to determine the neutron energy spectrum at various locations inside the ISS. The temperature-compensated spectrometer set used is the first to be developed specifically for space applications and its development is described in this paper. Results of the dose measurements indicate that the dose received at two different depths inside the phantom is not significantly different, suggesting that bubble detectors worn by a person provide an accurate reading of the dose received inside the body. The energy spectra measured using the spectrometer are in good agreement with previous measurements and do not show a strong dependence on the precise location inside the station. To aid the understanding of the bubble-detector response to charged particles in the space environment, calculations have been performed using a Monte-Carlo code, together with data collected on the ISS. These calculations indicate that charged particles contribute <2% to the bubble count on the ISS, and can therefore be considered as negligible for bubble-detector measurements in space.