I expect that the floor of the bin is elastic in the technical sense - it returns to its resting form when no force is applied. When the BANG goes off the base of the bin is compressed into the floor, hard. This lowers its center of gravity. Then it returns to its previous shape, the CoG rising as it does so. Once it has returned to its original position it discovers, rather to its surprise, that it's now travelling upwards, and so it continues to do so.

You also have less pressure inside the bin than outside.

I think the shock wave travels through the bottom of the bin, bounces off the hard concrete floor and back to hit the bucket, thereby lifting it up.

As well as the shockwave mentioned elsewhere, you also have pressure effects.

The initial explosion drops the pressure in the bin below atmospheric pressure. Assuming there's enough kick to separate the bin from the floor, you've got a higher pressure pressing up on the bottom from below than down from inside the container, so the bin accelerates up.

I'm not sure if it'd be a significant effect, however.