In this case come is not a finite verb but a participle. If you want to paraphrase the clause it heads as a relative clause you should cast it in the perfect construction:
. . . a nightingale which has come over on the Cunard or White Star Line.
In grammatical fact, however, this is an adjectival use of the participle. Today we rarely use the participles of intransitive verbs adjectivally—the adjectival participle is usually passive in sense. But at one time the perfects of verbs of motion were routinely expressed with BE rather than HAVE, and the participles acted simultaneously as perfects and predicative complements.
Joy to the world! The Lord is come.
This use still survives in expressions like "John is gone."
Fitzgerald's use is paralleled in Hamlet:
There needs no ghost, my lord, come from the grave / To tell us this