Analyze the connection between the fish and the rod and the relationship between Sheila and the narrator.
In "The Bass, the River, and Sheila Mant," the narrator has equal desires to "obtain" a bass and the affections of Sheila Mant. When the narrator finally works up the nerve to ask Sheila to a local dance, she agrees to go, and it seems that the boy has at least been successful with one of his goals.
On the way to the dance, Sheila and the narrator travel by boat, and the narrator leaves a line dangling from his rod. This demonstrates that he is willing to sacrifice one of his "loves" (fishing) for another (Sheila). Soon, though, the boy realizes that he can't have both. He struggles to pay attention to Sheila's self-centered rambling even as a huge bass has been hooked and begs for his attention.
Ultimately, because Sheila has expressed her disdain for fishing, the boy must decide between aggressively pursuing the fish on his line or cutting it loose so that he can pay attention to Sheila. He chooses Sheila--a poor choice because she leaves him once they arrive at the dance and ends up going home with an older boy.
Sheila and the fish are similar; they both represent what the boy longs for, but they are not easily obtained (at least not when you're a young teen going after a more mature girl!). They string the boy along--Sheila uses him to get to the dance and most likely because she enjoys playing the younger boy; similarly, the fish, though it's on the end of the boy's line, seems to be the one stringing him along and tempting the narrator to pursue it.