Creating additional value out of biogas during waste treatment has become a priority in past years. Biogas bioconversion into valuable bioproducts such as biopolymers has emerged as a promising strategy. This work assessed the operational feasibility of a bubble column bioreactor (BCB) implemented with gas recirculation and inoculated with a polyhydroxybutyrate (PHB)-producing strain using biogas as substrate. The BCB was initially operated at empty bed residence times (EBRTs) ranging from 30 to 120 min and gas recirculation ratios (R) from 0 to 30 to assess the gas-to-liquid mass transfer and bioconversion of CH4. Subsequently, the BCB was continuously operated at a R of 30 and an EBRT of 60 min under excess of nitrogen and nitrogen feast-famine cycles of 24 h:24 h to trigger PHB synthesis. Gas recirculation played a major role in CH4 gas–liquid transfer, providing almost fourfold higher CH4 elimination capacities (~41 g CH4 m−3 h−1) at the highest R and EBRT of 60 min. The long-term operation under N excess conditions entailed nitrite accumulation (induced by O2 limiting conditions) and concurrent methanotrophic activity inhibition above ~60 mg N-NO2− L−1. Adjusting the N-NO3− supply to match microbial N demand successfully prevented nitrite accumulation. Finally, the N feast-famine 24 h:24 h strategy supported a stable CH4 conversion with a removal efficiency of 70% along with a continuous PHB production, which yielded PHB accumulations of 14.5 ± 2.9% (mg PHB mg−1 total suspended solids × 100). These outcomes represent the first step towards the integration of biogas biorefineries into conventional anaerobic digestion plants.