What does the fish most likely symbolize in Elizabeth Bishop's poem, "The Fish"?

Well, the first option is that the fish doesn't symbolize anything at all. Never leave that option out, even in poetry. Some poems try to capture vivid experiences in vivid verse.  In that reading, the poet caught a fish that looked strange, stared at it, and let it go. Again, don't underestimate that. Confronting other forms of life can be striking and meaningful without metaphor.

But if we assume it is a metaphor, then we find its meaning in those vivid images: the beard, the speckling, the loose skin, the multiple fishhooks, the scarring, etc. In catching a fish, the narrator has accidentally confronted age and mortality. The fish looks old and scarred by life, and if she keeps it, it dies. Releasing it lets life continue (and denies mortality).