Arterial spin labeled cardiovascular magnetic resonance (ASL-CMR) is a non-contrast myocardial perfusion imaging technique, which can detect angiographically significant coronary artery disease. Sensitivity of ASL-CMR can be improved by shortening the imaging window with parallel imaging which reduces physiological noise from cardiac motion. In this work, we explore the optimal Cartesian sampling pattern and parallel imaging reconstruction strategy for bSSFP ASL-CMR. We consider different under-sampling masks, acceleration factors, and reconstruction techniques to minimize the imaging window. The optimal setting is selected based on the bias in MP measurements.