The title sets up a joke that turns serious: a doctor's "bedside manner" is how he talks to the sick, and here the sea plays that part. It is "fine-spoken and rough" at once, polite and gruff, soothing and harsh, like a physician who says hard things gently. The speaker calls it "a physician for the soul," so the sea seems to heal something that isn't physical.
The second stanza is stranger. "I hear/do not hear it" suggests the sound comes and goes, or that the speaker is unsure whether they're really listening or only remembering. The slash makes the sentence flicker. "Again and again" echoes the rhythm of waves. The last line, "every place I could not / open my eyes," implies the speaker has been in dark or painful moments, eyes shut, perhaps in grief or fear, and the sea was still there as a sound. The mood is quiet, tender, and a little uncertain: comfort that is real but never fully clear.