West Antarctic ice shelves have thinned dramatically over recent decades. Oceanographic measurements that explore connections between offshore warming and transport across a continental shelf with variable bathymetry toward ice shelves are needed to constrain future changes in melt rates. Six years of seal-acquired observations provide extensive hydrographic coverage in the Bellingshausen Sea, where ship-based measurements are scarce. Warm but modified Circumpolar Deep Water floods the shelf and establishes a cyclonic circulation within the Belgica Trough with flow extending toward the coast along the eastern boundaries and returning to the shelf break along western boundaries. These boundary currents are the primary water mass pathways that carry heat toward the coast and advect ice shelf meltwater offshore. The modified Circumpolar Deep Water and meltwater mixtures shoal and thin as they approach the continental slope before flowing westward at the shelf break, suggesting the presence of the Antarctic Slope Current. Constraining meltwater pathways is a key step in monitoring the stability of the West Antarctic Ice Sheet.