In American and Canadian English, tidbit is the preferred spelling of the noun referring to (1) a choice morsel or (2) a pleasing bit of something. Titbit is preferred everywhere else. Neither spelling is right or wrong. Titbit is older, but tidbit is etymologically justifiable (the first syllable likely comes from the archaic colloquialism tid, meaning tender). And tidbit is not so new itself; it was well established in American English by the early 1800s.
While researching the Marquis de Sade several years ago, I came across an intriguing biographical tidbit. [New York Times]
Any mixed messages to be had from that tattoo-related tidbit are easy to clear up, however. [Vancouver Sun]
Press a button, and you’ll unlock a tidbit about a particular town. [Washington Post]
Outside North America
Apart from a few titbits about his lavish travel expenses, there were questions about his friendship with dodgy dictators and arms dealers. [Guardian]
One titbit concerned the 12th hole, which has played as the second most difficult in the tournament so far. [Irish Times]
Still, Moore has a remarkable memory for past conversations and the juicy titbit. [Sydney Morning Herald]