Oh boy, the dreaded BBB!
First, if you don't *have* to switch to a BBB and still have the option of using the cot, you may decide to take a break from the transition for a month or so, and let him mature a bit. This has worked for a number of my friends. Every kid is ready at a different age. For some, the freedom provided by the BBB is just too much for their little bodies to handle!
If you are determined to transition to BBB now, then consistency is vital. At age 2 you can introduce reward charts to reinforce the behavior you want. So, if he stays in his bed at night, then he gets a sticker. After 3 stickers he gets some kind of small prize (I usually use matchbox cars). After 5-6 stickers he gets an even bigger prize (we usually take a trip to McDonald's or something). 2 year olds are REALLY motivated by stickers. You'd be amazed at what they'll do for one! Imagine the sticker is a really big Margarita, and think of all that you'd do for a nice one after a hard day with a toddler!
You might also give him things to do in his bed. Give him a flashlight and tell him he can use that to read books while sitting in bed. The first time he's out of bed, no more flashlight. You can take him shopping for special bedding or a special bedtime friend. Really stress that he's such a big boy. Talk about how you and daddy stay in bed at night, etc. But I think that you don't go up every 10 minutes to put back in bed. That's reinforcing negative behavior. It's more important to ignore it, let him fall asleep on the floor if he wants to, and reward the good behavior.
One note on a reward chart: Toddlers don't have the best memories and are also really visual. So, it's important to SHOW him the chart at bedtime, and even show him the stickers he can earn. You can be really excited about it, and I think that will help.
GL! Keep us posted!