I can't write your letter for you, but you might want to include the following points.
Collins would include a description of the setting.... the sound of the guns, the conditions, the sights.
"The dark uniforms of the men were so coated with dust from the incessant wrestling of the two armies that the regiment almost seemed a part of the clay bank which shielded them from the shells."
"For the little meadow which intervened was now suffering a terrible onslaught of shells. Its green and beautiful calm had vanished utterly. Brown earth was being flung in monstrous handfuls. And there was a massacre of the young blades of grass. They were being torn, burned, obliterated."
Note: Collins was so focused on his thirst that he seems unfazed by the death and carnage around him.
From the text, we see that Collins is looked upon like the youth he is..... they laugh at him, don't believe he'll leave for the water, and even taunt him a bit. In your letter, you might use the laughter and taunting as an excuse when he writes his family. "I did it because....."
As far as the act itself, it wouldn't take you an enormous amount of time to expound upon what is written in the text. In terms of Collins brush with death, you can go in two directions because we don't know what his reaction to the bucket spilling actually was. One, Collins is angry at his comrades.... two, he realizes what he's done and is angry at himself for taking such a chance, only to have it be for nothing.