Leaving Gibbon’s sneering atheism, he’s still a good basic source on the linguistic map of the Empire:
http://ancienthistory.about.com/library/bl/bl_text_gibbon_1_2_2.htm
“The language of Virgil and Cicero, though with some inevitable mixture of corruption, was so universally adopted in Africa, Spain, Gaul Britain, and Pannonia, that the faint traces of the Punic or Celtic idioms were preserved only in the mountains, or among the peasants. Education and study insensibly inspired the natives of those countries with the sentiments of Romans; and Italy gave fashions, as well as laws, to her Latin provincials. They solicited with more ardor, and obtained with more facility, the freedom and honors of the state; supported the national dignity in letters and in arms; and at length, in the person of Trajan, produced an emperor whom the Scipios would not have disowned for their countryman. The situation of the Greeks was very different from that of the barbarians. The former had been long since civilized and corrupted. They had too much taste to relinquish their language, and too much vanity to adopt any foreign institutions. Still preserving the prejudices, after they had lost the virtues, of their ancestors, they affected to despise the unpolished manners of the Roman conquerors, whilst they were compelled to respect their superior wisdom and power. Nor was the influence of the Grecian language and sentiments confined to the narrow limits of that once celebrated country. Their empire, by the progress of colonies and conquest, had been diffused from the Adriatic to the Euphrates and the Nile. Asia was covered with Greek cities, and the long reign of the Macedonian kings had introduced a silent revolution into Syria and Egypt. In their pompous courts, those princes united the elegance of Athens with the luxury of the East, and the example of the court was imitated, at an humble distance, by the higher ranks of their subjects. Such was the general division of the Roman empire into the Latin and Greek languages. To these we may add a third distinction for the body of the natives in Syria, and especially in Egypt, the use of their ancient dialects, by secluding them from the commerce of mankind, checked the improvements of those barbarians. The slothful effeminacy of the former exposed them to the contempt, the sullen ferociousness of the latter excited the aversion, of the conquerors. Those nations had submitted to the Roman power, but they seldom desired or deserved the freedom of the city: and it was remarked, that more than two hundred and thirty years elapsed after the ruin of the Ptolemies, before an Egyptian was admitted into the senate of Rome.”
Having said all that, is entirely plausible, perhaps even likely, that Pilate conducted his trial of Jesus, as an official act of Roman potestas, in Latin.