Hit Fit (BJJ), Can Sönmez, Bristol, UK - 13/03/2014
As a rule of thumb, if you're underneath, you don't want to be flat on your back. So, start your elbow escape by turning to your side, getting a shoulder off the floor. Saulo notes that you should be doing this as early as possible: if they are working to mount from side control, set up your escape during the transition, rather than waiting for them to secure their mount. Work an elbow inside their knee and set up your frame, in order to push into the leg.
There are several ways of framing for that push. I personally like to keep defending my neck throughout, using my elbows to dig into their leg. That keeps my neck safe, but it does limit your range and reduce leverage: you'll need to curl in towards their leg to generate enough push. The other main option is to extend your arms further towards their hip, leaving your neck vulnerable but considerably beefing up your leverage. That frame is also handy for stopping them moving up higher in mount.
When I went to the seminar with the Dutch black belt under Rickson, Michel Verhoeven, he began by reaching across to their opposite hip with his hand, keeping his arm slightly bent. He then pushed on the hip: if they were higher up, he would form a frame with his arms and push. That second option is the one my fellow Artemis BJJ co-founder Dónal likes to teach, putting one arm across their hip (the hand is by one hip, the elbow by their other hip). For extra leverage, brace that first arm with your other hand, against your wrist. Stephan Kesting recommends keeping the hand of the hip-arm in a fist, to lock in the grip (so your second hand doesn't slide off as easily).
Whichever option you use, the idea is to make enough space from the combination of your shrimp and bridge to pull your leg through. As with side control escapes, don't just bridge and plop back down, it needs to combine with your shrimp. The leg you're trying to pull free should be flat: if it isn't, they will be able to trap it with their leg. Having that leg flat also makes it easier to pull out. You other foot will be on the floor with the knee raised, in order to provide the push for your shrimp.
After you're on your side, bump slightly, then pry their leg open with your elbow. Aim to pop your knee through between their legs initially. If you can pull the whole leg out in one, great, but don't be greedy. Getting that first knee through will mean you can then brace your leg against their thigh, aiding your second shrimp to free your other leg. Once one of your legs is fully out, you can then use it to wrap around one of theirs and hook under their leg with your instep, or put your free leg around their back (be sure to clamp down if you do that).
You now have the option of moving to half guard (especially if you've wrapped their leg, you're basically there already), open guard (e.g., butterfly) or continue working for full guard. As with escapes under side control, keep shrimping until you have the room to pull your leg free. Even if you can't wrap their leg, you can jam your outside leg tight to theirs, then use that for your base to shrimp.
Teaching & Sparring Notes: Small class today, but brought up some interesting points nevertheless. The guy I was drilling with mentioned he had an MMA fight in May, so he liked the look of the version I use, with my arms still up near my head. I had never considered how that might be useful from an MMA perspective, because you can still protect yourself from punches that way. However, I am in no way qualified to teach MMA, so I certainly wouldn't want to make any claims about the efficacy of one option over the other inside a cage/ring. ;)
It was also useful for me on top, as I continued to work on getting my knees up high by their head. My problem is that my legs keep slipping back down, it's hard to lock them in place. I could try pushing off my toes slightly, but then I'd be worried about losing purchase on their sides (as I'm clamping the soles of my feet to their sides as I walk up the body for a high mount).
Something potentially helpful I tried was using the arm I had under their head to grab their other arm, pulling it in by their head. That opens up some more space for me to bring my knee up further, which is handy. I'll be playing with that more in future.