We introduce a formal experimental design methodology for guiding the placement of drifters to infer ocean currents. The majority of drifter placement campaigns either follow standard `space-filling' designs or relatively ad-hoc expert opinions, which could be significantly improved on by appealing to statistical experimental design. Drifter observations follow a Lagrangian structure as drifters are advected through the Eulerian vector field. It is, therefore, important to consider the likely future trajectories of placed drifters to compute the utility of candidate measurement locations. We present BALLAST: Bayesian Active Learning with Look-ahead Amendment for Sea-drifter Trajectories, a novel light-weight, nonmyopic policy amendment for drifter trajectory data that can be appended to any myopic policy. Our numerical studies suggest substantial benefits in incorporating BALLAST into the sequential placement strategies of drifters.