There is a growing interest in leveraging tactile sensing and data-driven models to enable robust robotic grasping; in this context, detecting object slip is a fundamental skill. However, the large variability in gripper-object interactions (e.g. different grasp poses, area of contact with the sensor, and directions of slip) makes the collection of suitable data to train models costly in time and resources, and current data collection protocols are oversimplified to several repetitions on a small subset of gripper-object interactions. To address this challenge, we propose DENSE, an efficient and highly reproducible protocol which is designed to capture this large variability by exploring gripper-object interactions across the object surface, and which automatically embeds straightforward labelling. We show experimentally that, compared to baseline methods, the DENSE protocol can reduce time effort by up to 50%, and models trained with the collected data improve up to 85% in their generalisation to unseen gripper-object interactions.