Context. The host galaxies of gamma-ray bursts (GRBs) have been claimed to have experienced a recent inflow of gas from the intergalactic medium. This is because their atomic gas distribution is not centred on their optical emission and because they are deficient in molecular gas given their high star formation rates (SFRs). Similar studies have not been conducted for host galaxies of relativistic supernovae (SNe), which may have similar progenitors. Aims. The potential similarity of the powering mechanisms of relativistic SNe and GRBs allowed us to make a prediction that relativistic SNe are born in environments similar to those of GRBs, that is, ones which are rich in atomic gas. Here we embark on testing this hypothesis by analysing the properties of the host galaxy NGC 3278 of the relativistic SN 2009bb. This is the first time the atomic gas properties of a relativistic SN host are provided and the first time resolved 21 cm-hydrogen-line (H I) information is provided for a host of an SN of any type in the context of the SN position. Methods. We obtained radio observations with the Australia Telescope Compact Array (ATCA) covering the H I line, and optical integral field unit spectroscopy observations with the Multi Unit Spectroscopic Explorer (MUSE) at the Very Large Telescope (VLT). Moreover, we analysed archival carbon monoxide (CO) and multi-wavelength data for this galaxy. Results. The atomic gas distribution of NGC 3278 is not centred on the optical galaxy centre, but instead around a third of atomic gas resides in the region close to the SN position. This galaxy has a few times lower atomic and molecular gas masses than predicted from its SFR. Its specific SFR (sSFR ≡ SFR/M*) is approximately two to three times higher than the main-sequence value, placing it at the higher end of the main sequence, towards starburst galaxies. SN 2009bb exploded close to the region with the highest SFR density and the lowest age, as evident from high Hα EW, corresponding to the age of the stellar population of ~5.5 Myr. Assuming this timescale was the lifetime of the progenitor star, its initial mass would have been close to ~36 M⊙. Conclusions. As for GRB hosts, the gas properties of NGC 3278 are consistent with a recent inflow of gas from the intergalactic medium, which explains the concentration of atomic gas close to the SN position and the enhanced SFR. Super-solar metallicity at the position of the SN (unlike for most GRBs) may mean that relativistic explosions signal a recent inflow of gas (and subsequent star formation), and their type (GRBs or SNe) is determined either (i) by the metallicity of the inflowing gas, so that metal-poor gas results in a GRB explosion and metal-rich gas (for example a minor merger with an evolved galaxy or re-accretion of expelled gas) results in a relativistic SN explosion without an accompanying GRB, or (ii) by the efficiency of gas mixing (efficient mixing for SN hosts leading to a quick disappearance of metal-poor regions), or (iii) by the type of the galaxy (more metal-rich galaxies would result in only a small fraction of star formation being fuelled by metal-poor gas).