escaping side mount from a bigger guy was something I really had to work on, but my teacher gave me some excellent pointers:
1. don't be a flailing fish - alot of guys buck incessantly to the point where they're just bucking to buck, just trying to push the guy off so they can get a breath and go right back to the same position. Well that's fine, you got your breath for a half second, but now he's crushing you again and your winded. You're never going to throw a bigger guy off you on the first bump unless he's just fat and you're just lucky and cockstrong. Bump deliberately and to create space, if he underhooks you, bump until you can slip your arm under his. make a little space every time. don't just flail around under there.
2. Don't panic - he's on top of you, you can't breathe good, it's uncomfortable. deal with it, try to focus on what you need to do and not what's happening to you. Panicing gets you excited, gets your heart rate up, makes you lose focus, etc. You don't want that.
3. Pay attention to his grips, they're a tell-all - How does he have you gripped? Collar and hip? Hands clasped with underhook? You can tell alot about what a guy is going to do by how he grips you.
4. This sorta goes with number one, but make space - Use your hips and your bumps to make space, space = air, air = breathing, breathing = good.
5. Find the right times to explode: Every motion doesn't have to be a hail mary all or nothing backbusting bridge, but some of them do. When you shrimp to half guard, SHOOT your knee in there, don't just lolligag it across. As a rule, big guys are slow, so sometimes even when they know what you're doing, if you're slick and explosive, they can't stop it.
hope this helps.