Well, the results are in, and with your help I won the Best Jewish Religious Blog award! I would like to thank you all publicly - בפומבי b'fumbei.
The word pumbei פומבי first appears in Talmudic times, and means "publicity". In modern Hebrew we also find the adjective pumbi - "public".
The word was borrowed from the Greek pompe, which meant "a solemn procession", and gave us the English words pomp and pompous. Take Our Word For It discusses "pompous":
It comes, through French, from the same source as pomp, which is Latin pompa. The Romans acquired the word from Greek pompe "a sending," coming ultimately from the root pempein "to send". Greek pompe came to be used figuratively for something that was "sent forth", namely a procession or parade. As such processions were often either very solemn or quite splendid, the notions of "a display" and then "an ostentatious display" came to be attached to the Greek word. Those meanings passed into Latin and eventually into English, though the "procession" meaning died out in English by the early 19th century, such that now the word carries only the "showy" meaning, which had taken on a negative air as early as Chaucer's time (the late 14th century).
As an aside, I'd like to point out that many people found the campaigning for votes in the JIB awards ostentatious and perhaps even pompous. But as I wrote earlier, there was no prize being offered in the contest, only publicity. And in a contest by people who put themselves in the public (you don't find too many shy bloggers), where the reward is more publicity, I fail to see the problem with a public campaign for votes! So while pumbei and "pompous" may be related etymologically, I don't think there's a causal relationship between them...