We propose a nonwearable hydraulic bed sensor system that is placed underneath the mattress to estimate the relative systolic blood pressure of a subject, which only differs from the actual blood pressure by a scaling and an offset factor. Two types of features are proposed to obtain the relative blood pressure, one based on the strength and the other on the morphology of the bed sensor ballistocardiogram pulses. The relative blood pressure is related to the actual by a scale and an offset factor that can be obtained through calibration. The proposed system is able to extract the relative blood pressure more accurately with a less sophisticated sensor system compared to those from the literature. We tested the system using a dataset collected from 48 subjects right after active exercises. Comparison with the ground truth obtained from the blood pressure cuff validates the promising performance of the proposed system, where the mean correlation between the estimate and the ground truth is near to 90% for the strength feature and 83% for the morphology feature.