18 FDG PET/CT imaging is commonly used in diagnosis and follow-up of metastatic breast cancer, but its quantitative analysis is complicated by the number and location heterogeneity of metastatic lesions. Considering that bones are the most common location among metastatic sites, this work aims to compare different approaches to segment the bones and bone metastatic lesions in breast cancer. Two deep learning methods based on U-Net were developed and trained to segment either both bones and bone lesions or bone lesions alone on PET/CT images. These methods were cross-validated on 24 patients from the prospective EPICURE seinmeta metastatic breast cancer study and were evaluated using recall and precision to measure lesion detection, as well as the Dice score to assess bones and bone lesions segmentation accuracy. Results show that taking into account bone information in the training process allows to improve the precision of the lesions detection as well as the Dice score of the segmented lesions. Moreover, using the obtained bone and bone lesion masks, we were able to compute a PET bone index (PBI) inspired by the recognized Bone Scan Index (BSI). This automatically computed PBI globally agrees with the one calculated from ground truth delineations. Clinical relevance - We propose a completely automatic deep learning based method to detect and segment bones and bone lesions on 18 FDG PET/CT in the context of metastatic breast cancer. We also introduce an automatic PET bone index which could be incorporated in the monitoring and decision process.