Membership Inference (MI) poses a substantial privacy threat to the training data of Automatic Speech Recognition (ASR) systems, while also offering an opportunity to audit these models with regard to user data. This paper explores the effectiveness of loss-based features in combination with Gaussian and adversarial perturbations to perform MI in ASR models. To the best of our knowledge, this approach has not yet been investigated. We compare our proposed features with commonly used error-based features and find that the proposed features greatly enhance performance for sample-level MI. For speaker-level MI, these features improve results, though by a smaller margin, as error-based features already obtained a high performance for this task. Our findings emphasise the importance of considering different feature sets and levels of access to target models for effective MI in ASR systems, providing valuable insights for auditing such models.