In the story "The Bass, the River, and Sheila Mant", how does the setting---which I believe is the river, mostly---play a major role in the...

You're certainly on track with what you've pointed out from the story.  A couple of elements to consider are that the narrator is more comfortable on the river than he is on land.  Notice that when he tries to play softball, he's awkward.  When he's with Sheila at the dance, he's awkward, and she leaves him for an older boy.  But, on the river, he prepares his boat as best as possible to take Sheila to the dance, and he is confident in his angler skills.

Another important point about the river is that, as you pointed out, the boy must choose between the two parts of his life that he holds dear, both of which are connected with the river.  The narrator associates Sheila with the river because she's always sunbathing near it when he's fishing, and of course, the river is the home of his hobby.  So, it is ironic and fitting that the narrator has to choose between his two "loves" when he takes Sheila out on a date and that he has to make his choice while on the river.