Multipartite viruses package their genomic segments independently and thus incur the risk of being unable to transmit their entire genome during host-to-host transmission if they undergo severe bottlenecks. In this paper, we estimated the bottleneck size during one infection cycle of Faba bean necrotic stunt virus (FBNSV), an octopartite nanovirus whose segments have been previously shown to converge to particular and unequal relative frequencies within host plants and aphid vectors. Two methods were used to derive this estimate, one based on the probability of transmission of the virus and the other based on the temporal evolution of the relative frequency of markers for two genomic segments, one frequent and one rare (segment N and S, respectively), both in plants and vectors. Our results show that FBNSV undergoes severe bottlenecks during aphid transmission. Further, even though the bottlenecks are always narrow under our experimental conditions, they slightly widen with the number of transmitting aphids. In particular, when several aphids are used for transmission, the bottleneck size of the segments is also affected by within-plant processes and, importantly, significantly differs across segments. These results indicate that genetic drift not only must be an important process affecting the evolution of these viruses but also that these effects vary across genomic segments and, thus, across viral genes, a rather unique and intriguing situation. We further discuss the potential consequences of our findings for the transmission of multipartite viruses.