In "The River Merchant's Wife," it's appropriate that this monologue/letter is written in isolation. There are no other people around that we know of, and monkeys and moss just don't count as companions (at least, that's what they told us at our junior high prom). It's almost as if the natural world and landscape have completed the task of isolating the wife that her husband's departure began. Her isolation seems so complete, in fact, that it seems integral to the observations that she shares in the poem.
The speaker is isolated on account of her own bashfulness and innocence in the first stanza, but marriage—however uncomfortable at first—helps her to overcome this. Good for her!
The isolation that the woman feels has its roots in her rural childhood upbringing. (It's not your fault, hubby!)