We present MooseNet, a trainable speech metric that predicts the listeners' Mean Opinion Score (MOS). We propose a novel approach where the Probabilistic Linear Discriminative Analysis (PLDA) generative model is used on top of an embedding obtained from a self-supervised learning (SSL) neural network (NN) model. We show that PLDA works well with a non-finetuned SSL model when trained only on 136 utterances (ca. one minute training time) and that PLDA consistently improves various neural MOS prediction models, even state-of-the-art models with task-specific fine-tuning. Our ablation study shows PLDA training superiority over SSL model fine-tuning in a low-resource scenario. We also improve SSL model fine-tuning using a convenient optimizer choice and additional contrastive and multi-task training objectives. The fine-tuned MooseNet NN with the PLDA module achieves the best results, surpassing the SSL baseline on the VoiceMOS Challenge data.