To be honest, I was breeding dubias in a rubbermaid bin in my dorm. One escaped and I found the nymph in my bed. Luckily it wasn't even half an inch yet. But I've only ever had one get out, and I believe it to be because my egg crates were stacked pretty high, touching the lid.
Also, they can climb certain plastic containers. Feel the sides of a bin before you by it - it needs to be absolutely baby smooth, or you're going to have to tape around the top edges (which is really easy- double sided tape is easiest) or use the vaseline trick, which I think is gross.
Never set out sticky traps in a reptile room, though. I had a mass cricket escape a long time ago and set out a sticky trap - probably about 200 two weekrs that got out of my order of 1000 crickets, which was poorly packed. I also had a reptile escape the same day without realizing, and found my poor small iguana on the sticky trap when I got home. Two hours and a cup of vegetable oil later, he was off and fine, but I will never set out bug traps again. A child's mistake, but still.
So if you're worried, definitely go for taping around the edges. That's your best bet. However, if you bin is tall enough and smooth enough, the likelihood of them getting out is very small. Keep the area lighted and them well fed and you'll find that they don't want to even leave the tub anyway.
They love paper towel tubes as much as egg crates, and both of those are free. Don't be one of those people that wastes money on ordering crates - you can ask for a hundred from your local grocery store. They're just going to be recycled anyway.