Magnetic Resonance (MR) imaging, despite its proven diagnostic utility, remains an inaccessible imaging modality for disease surveillance at population-level. A major factor rendering MR inaccessible is lengthy scan times. An MR scanner collects data in the Fourier space, called the k-space, of the underlying anatomy. Creating a high-fidelity image requires a large amount of samples, increasing the scan time. To accelerate MR scans for disease surveillance, recent works have shown the feasibility of bypassing image reconstruction and directly learning to detect disease directly from a sparse learned subset of the k-space measurements. In this work, we propose Adaptive Sampling for MR (ASMR), an adaptive sampling method that learns a policy to sequentially select k-space samples to optimize for target disease detection. For 6/8 pathology classification tasks in Knee, Brain, and Prostate MR scans, ASMR reaches within 2% of the performance a fully sampled classifier, while using only 8% of the samples. Further, ASMR offers substantial benefits over prior state-of-the-art work in k-space sampling such as EMRT, LOUPE, and DPS.