Sheila is a large part of the narrator's external conflict. Sheila doesn't like the water and she doesn't like fishing. The narrator loves both. He knows that engaging in his favorite hobby—fishing—won't make her happy and will end their budding relationship. Sheila and the narrator both want different things, and their desires clash in the story.
The narrator's internal conflict is his desire to fish and catch the beautiful bass he sees in the river. He knows he may never again get a chance at such a perfect fish. However, his desire to catch it fights with his desire to please Sheila. None of this is spoken to the object of his desire. He tries to focus on her boring, self-centered conversation while his mind is pulled to the bass again and again.
The river operates as a setting for his internal and external conflict. The river is what he has to navigate to get her to the party; it also makes it more difficult for him to successfully fulfill his objective with regards to his primary external conflict: pleasing Sheila. If they'd taken a car, the conflicts the narrator struggles with wouldn't have occurred.