The stability of arc bubble is a crucial indicator of underwater wet welding process. However, limited research exists on detecting arc bubble edges in such environments, and traditional algorithms often produce blurry and discontinuous results. To address these challenges, we propose a novel arc bubble edge detection method based on deep transfer learning for processing underwater wet welding images. The proposed method integrates two training stages: pre-training and fine-tuning. In the pre-training stage, a large source domain dataset is used to train VGG16 as a feature extractor. In the fine-tuning stage, we introduce the Attention-Scale-Semantics (ASS) model, which consists of a Convolutional Block Attention Module (CBAM), a Scale Fusion Module (SCM) and a Semantic Fusion Module (SEM). The ASS model is further trained on a small target domain dataset specific to underwater wet welding to fine-tune the model parameters. The CBAM can adaptively weight the feature maps, focusing on more crucial features to better capture edge information. The SCM training method maximizes feature utilization and simplifies training by combining multi-scale features. Additionally, the skip structure of SEM effectively mitigates semantic loss in the high-level network, enhancing the accuracy of edge detection. On the BSDS500 dataset and a self-constructed underwater wet welding dataset, the ASS model was evaluated against conventional edge detection models-Richer Convolutional Features (RCF), Fully Convolutional Network (FCN), and UNet-as well as state-of-the-art models LDC and TEED. In terms of Mean Absolute Error (MAE), accuracy, and other evaluation metrics, the ASS model consistently outperforms these models, demonstrating edge detection capabilities that are both effective and stable in detecting arc bubble edges in underwater wet welding images.