Abstract Axisymmetric dust rings are a ubiquitous feature of young protoplanetary disks. These rings are likely caused by pressure bumps in the gas profile; a small bump can induce a traffic-jam-like pattern in the dust density, while a large bump may halt radial dust drift entirely. The resulting increase in dust concentration may trigger planetesimal formation by the streaming instability (SI), as the SI itself requires some initial concentration of dust. Here we present the first 3D simulations of planetesimal formation in the presence of a pressure bump modeled specifically after those seen by Atacama Large Millimeter/submillimeter Array. We place a pressure bump at the center of a large 3D shearing box, along with an initial solid-to-gas ratio of Z = 0.01, and we include both particle back-reaction and particle self-gravity. We consider millimeter-sized and centimeter-sized particles separately. For simulations with centimeter-sized particles, we find that even a small pressure bump leads to the formation of planetesimals via the SI; a pressure bump does not need to fully halt radial particle drift for the SI to become efficient. Furthermore, pure gravitational collapse via concentration in pressure bumps (such as would occur at sufficiently high concentrations and without the SI) is not responsible for planetesimal formation. For millimeter-sized particles, we find tentative evidence that planetesimal formation does not occur. If this result is confirmed at higher resolution, it could put strong constraints on where planetesimals can form. Ultimately, our results show that for centimeter-sized particles planetesimal formation in pressure bumps is extremely robust.