He gets on top of the bucket and jumps up to the bars and manages to unlock the gate and climb out.
Notice how the camera cuts to Jesse’s legs swinging about after making the jump and hanging from the ceiling (twice). The way it is done looks eerily similar to how someone’s legs flail around for support after hanging them self. Also, he is jumping off of a bucket (the origin of the phrase “kick the bucket” likely came from the practice of tying a noose around your neck, standing on a bucket, knocking it over, then suffocating to death).
This imagery is repeated later in the episode when Walt drops the pay phone after calling the DEA office; the phone starts swinging around in the same manner. Neither Walt nor Jesse has much to live for at this point, so it is not out of the question for either one of them to off themselves. This wouldn’t be the first time the show has made some type of foreshadowing to the character’s deaths: Jesse was shown holding a DEA mug, which when shown with the handle spells out “DEAD”, and Walt sees a bullet hole in the forehead of his reflection in “Ozymandias”.
Making the best of a bad situation, a few Reddit users have brought to light that there’s always a chance that this could earn Aaron Paul his own line of Jordans — Air Pinkman coming to a store near you.
To help improve the meaning of these lyrics, visit "Granite State" by Breaking Bad (Ft. Peter Gould) and leave a comment on the lyrics box