All right y'all, I made this account specifically to ask this question because it's killing me trying to find this story.
I thought it was an Ursula K Le Guin thing but maybe not.
It's set on a space station, and the MC/narrator is some kind of officer in some space agency (Starfleet-style). An alien ship comes in to negotiate entry into the equivalent of the Federation.
The ship itself is a biological organism, as are all the components within it.
There's also an Ambassador, who as far as I remember is quite short and possibly white-furred. The ship docks with the station by means of a sphincter that opens and closes to let people through.
The Ambassador comes onto the station, the MC meets them, and...stuff happens. There are some lines about the relative merits of artificial machines vs. biological ships and components. That's all I remember.
There's also a chance that this isn't a short story, but the beginning of a novel I picked up and only read a bit of.
Does this ring a bell for anyone?