Wikipedia suggests that the first mention of a bioship (an organic spaceship) was first mentioned as an idea in a 1953 short story "Specialist".
In the science fiction short story "Specialist" by Robert Sheckley, published in 1953 in Galaxy magazine, it is revealed that many galactic races are actually capable of symbiotic cooperation to become bioships, with each race forming a different part. Earth, apparently, is one of the planets inhabited by creatures that are supposed to function as FTL drives (Pushers), and, it is stated that all the conflicts and discontent of humanity are due to the fact that, while they have matured, they have nowhere to apply their true purpose. This story is perhaps the first mention of a bioship in science fiction.
And it mentions the alien spaceship Gomtuu as one of the first to appear in TV, but not necessarily as THE first to appear.
Is there any other earlier instance in flim or tv of an organic "bioship"? (Piloted by humans or not, either way)
I've narrowed this down to TV and Film, because without evidence to believe otherwise, I have no reason to doubt that the book example is probably the first in print.