Without sufficient space created, there is no escape. The bridge is your biggest weapon for creating the distance you need to move your hips back into guard. When your opponent makes it difficult to bridge by crossfacing tightly with Head and Underhook Control, you have no choice but to address the pressure first before fully escaping the Side Control. Relieve yourself from the weight on your face by pulling his tricep with your hand. However, it is important to use whatever bridge you can muster to reach his tricep, because simply reaching for it with your arm will expose your elbow to further control or possibly even submission.