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Quantitative volumetric evaluation of the placenta in fetal MRI scans is an important component of the fetal health evaluation. However, manual segmentation of the placenta is a time-consuming task that requires expertise and suffers from high observer variability. Deep learning methods for automatic segmentation are effective but require manually annotated datasets for each scanning sequence. We present a new method for bootstrapping automatic placenta segmentation by deep learning on different MRI sequences. The method consists of automatic placenta segmentation with two networks trained on labeled cases of one sequence followed by automatic adaptation using self-training of the same network to a new sequence with new unlabeled cases of this sequence. It uses a novel combined contour and soft Dice loss function for both the placenta ROI detection and segmentation networks. Our experimental studies for the FIESTA sequence yields a Dice score of 0.847 on 21 test cases with only 16 cases in the training set. Transfer to the TRUFI sequence yields a Dice score of 0.78 on 15 test cases, a significant improvement over the network results without transfer learning. The contour Dice loss and self-training approach achieve state-of-the art placenta segmentation results by sequence transfer bootstrapping.