An intense phytoplankton bloom forms over the continental shelf in the Ross Sea, Antarctica, every spring as the sea ice retreats during the expansion of the Ross Sea polynya. The extent of this bloom rarely covers the full area of the shelf for reasons that are not well understood. One clue may be found in satellite imagery spanning the last 25 years that shows frequently recurring, previously undescribed, large-scale plumes of high-chlorophyll water and jets of low-chlorophyll water demarking the northern boundary of the spring phytoplankton bloom. The plumes, with horizontal length scales of 100--200 km, appear at the same location each year. The spatial consistency of this pattern of jets and plumes suggests regulation by forcing that does not vary from year to year, such as the interaction between bathymetry and prevailing ocean currents. Here we present a modeling study indicating that this pattern in the spring phytoplankton bloom is caused by intrusions of offshore surface waters onto the continental shelf, guided by relatively deep polar shelf bathymetry. Our study suggests that currents from the Ross Sea gyre follow along the shelf break and prevent the phytoplankton bloom from extending farther toward the edge of the shelf, even when the waters there are ice-free, perhaps because the offshore waters have low iron concentrations. These results illustrate how phytoplankton distributions can be constrained by the interaction of deep bathymetry and surface geostrophic currents along the highly productive Antarctic continental shelf.