Bimanual manipulation with tactile feedback will be key to human-level robot dexterity. However, this topic is less explored than single-arm settings, partly due to the availability of suitable hardware along with the complexity of designing effective controllers for tasks with relatively large state-action spaces. Here we introduce a dual-arm tactile robotic system (Bi-Touch) based on the Tactile Gym 2.0 setup that integrates two affordable industrial-level robot arms with low-cost high-resolution tactile sensors. We present a suite of bimanual manipulation tasks tailored towards tactile feedback: bi-pushing, bi-reorienting, and bi-gathering. To learn effective policies, we introduce appropriate reward functions for these tasks and propose a novel goal-update mechanism with deep reinforcement learning. We also apply these policies to real-world settings with a tactile sim-to-real approach. Our analysis highlights and addresses some challenges met during the sim-to-real application, e.g. the learned policy tended to squeeze an object in the bi-reorienting task due to the sim-to-real gap. Finally, we demonstrate the generalizability and robustness of this system by experimenting with different unseen objects with applied perturbations in the real world. Videos are available at https://sites.google.com/view/bitouch-anonymous/.