While the present-day surface of Venus is certainly incompatible with terrestrial biology, the planet may have possessed oceans in the past and provided conditions suitable for the origin of life. Venusian life may persist today high in the atmosphere where the temperature and pH regime is tolerable to terrestrial extremophile microbes: an aerial habitable zone. Here we argue that on the basis of the combined biological hazard of high temperature and high acidity this habitable zone lies between 51 km (65 °C) and 62 km (-20 °C) altitude. Compared to Earth, this potential venusian biosphere may be exposed to substantially more comic ionising radiation: Venus has no protective magnetic field, orbits closer to the Sun, and the entire habitable region lies high in the atmosphere - if this narrow band is sterilised there is no reservoir of deeper life that can recolonise afterwards. Here we model the propagation of particle radiation through the venusian atmosphere, considering both the background flux of high-energy galactic cosmic rays and the transient but exceptionally high-fluence bursts of extreme solar particle events (SPE), such as the Carrington Event of 1859 and that inferred for AD 775. We calculate the altitude profiles of both energy deposition into the atmosphere and the absorbed radiation dose to assess this astrophysical threat to the potential high-altitude venusian biosphere. We find that at the top of the habitable zone (62 km altitude; 190 g/cm2 shielding depth) the radiation dose from the modelled Carrington Event with a hard spectrum (matched to the February 1956 SPE) is over 18,000 times higher than the background from GCR, and 50,000 times higher for the modelled 775 AD event. However, even though the flux of ionising radiation can be sterilizing high in the atmosphere, the total dose delivered at the top of the habitable zone by a worst-case SPE like the 775 AD event is 0.09 Gy, which is not likely to present a significant survival challenge. Nonetheless, the extreme ionisation could force atmospheric chemistry that may perturb a venusian biosphere in other ways. The energy deposition profiles presented here are also applicable to modelling efforts to understand how fundamental planetary atmospheric processes such as atmospheric chemistry, cloud microphysics and atmospheric electrical systems are affected by extreme solar particle events. The companion paper to this study, Constraints on a potential aerial biosphere on Venus: II. Solar ultraviolet radiation (Patel et al., in preparation), considers the threat posed by penetration of solar UV radiation. The results of these twin studies are based on Venus but are also applicable to extrasolar terrestrial planets near the inner edge of the circumstellar habitable zone.