Jailbait is a girl, usually attractive, under 18, someone you will go to jail for having sex with. It's not rare in America but I've never seen it abbreviated.

JB can also mean Jim Bean -- a type of alcohol... As in "a bottle of JB".

I have no idea for JB and Dido. Som.

I have a friend called JB, it can be short for Jean-Baptiste, a French name. It can also be slang for Jail Bait... Which means someone that is of bad influence to you... ex: A girl says to another girl: Don't talk to him, he's JB! But its not a very common expression. You should give an idea of where you saw that word, it could help.