Chapters 7-9 What event was going on that gave Bilbo the chance to put his plan into action?

Bilbo has a few plans. I think you might be referring to chapter 9. During a night of festivity, Bilbo saves his group by stealing the keys of the drunk jailer, unlocking the cells of the dwarves and helping them fit in a flotilla of empty wine barrels that are being floated downstream. Bilbo has some difficulties but he manages to stay afloat, clinging to the side of a barrel.