Two escapes from the bottom in side mount.
Here is the basic survival position from the bottom in side mount. First you want to block the full mount. If the opponent is on your right, put your right foot on your left knee and use your right knee to block the opponent getting his leg over for full mount. Create a frame with your arms, but keep them in tight to your torso until you can set the frame up. Still assuming the opponent is on your right, your right forearm goes against their belly, and the wrist and hand wraps around their hips to prevent them moving around to a north south position. (It’s important to keep this wrist out from under your opponent to avoid wrist locking yourself.) The left forearm frames against the opponent’s throat, with the hand grabbing the shoulder.
The first escape (written assuming your opponent is on your right) is for when they have their left arm under your head, and right arm over and holding under your shoulder. From the basic survival position, bump with a bridge and push to create enough space to shrimp and hip escape away. Keep your hold on both grips, left hand on the shoulder and right on the hip. Hip escape until you have enough space to pass your right knee in front of their body and across so you can lock up full guard. Locking the arms out can help to create enough space, also if the knee does get stuck you can still slowly work it across with some hip shifting.
The second escape is for when the opponent is blocking your hips on your right side with their right hand. This makes it easy for them to follow you before you can hip escape far. The escape starts the same, bump, push, shrimp and hip escape. Instead of trying to hip escape far away, bring your right knee over their right arm as soon as you can and place it across their chest. At this point you want to switch grips to control their left arm, gripping the triceps and wrist to prevent them from creating space and escaping the transition. Bring your left leg over the opponent’s head, and put it on their shoulder putting pressure on their back to control their posture. With the grip on their arm and the left leg holding them down you should be able to bring your right leg all the way through and place your right foot on their hip. Again, use this as part of the push/pull posture control. Now being the left leg back over the head and wrap it around to set up the closed guard. You can just let your right foot slide off their hip to lock it up as you pull the arm you’re controlling.