Right before Bruce Wayne attempts to leave the pit he packs up something in a towel and wraps it around his body.
Does anyone see what he packs?
When Bruce is packing up his stuff the doctor says the following to him.
Doctor: "Ah supplies for your journey. Oh that's, that's wonderful!"
So I imagine it contains things vital to stay alive once he leaves the pit such as food and water.
He packs some food. He's assuming he'll escape, but he needs provisions to survive on the surface, as he doesn't know where he is.
Bruce carries a bundle with him during the first trip. Although it is not shown what is it that he carries, nor is it mentioned in the Script.
This time Bruce does not carry anything, he simply walks determined to the ropeway and starts climbing.
INT. CAVE PRISON - MORNING Wayne puts some scraps of bread into a rough coat which he folds into a makeshift shoulder pack. PRISONER Supplies for your journey? Prisoners nearby laugh.
From the picture one can assume that the folded brown packets are food items and the other is a water container. So basically, he carried sustenance with him - food and water.
According to this copy of the script (p. 127):
Wayne puts some scraps of bread into a rough coat which he folds into a makeshift shoulder pack.
As the other answers point out, he is packing supplies (bread).
But why does he only packs in his third attempt?
I think it's because only in this third attempt he was determined to escape and save Gotham, this emphasizes that he was not in the right mind set before.