Machine Learning as a Service (MLaaS) holds significant importance in the field of technology and business due to its potential to democratise and simplify the deployment of machine learning models. MLaaS refers to providing machine learning tools, infrastructure, and algorithms as cloud-based services, allowing users to build, train, deploy, and manage machine learning models without needing to handle the underlying technical complexities. Selecting the right Machine Learning as a Service (MLaaS) provider for organisations requires a strategic approach considering the business's unique needs and goals. However, the MLaaS selection process is complex due to the need for complete information on the quality of services and MLaaS latent features such as model accuracy, explainability and intrinsic biases. In this paper, we propose a novel MLaaS Selection Framework (MSF) using incomplete QoS information available through service advertisement. We develop the knowledge-based bias detection and Explainable (B-XAI) framework to discover MLaaS latent features. The proposed framework builds a complete QoS profile of the providers using MLaaS advertisements, other user experiences, and short-term trial experiences. Finally, we apply the nearest neighbour algorithm to select the optimal MLaaS providers based on the users' preference models. Experiments with real-world datasets show the effectiveness of the proposed approach.