Is there a difference between "a little bit" and "a bit"? --> I guess it's the in the urgency of something (or at least how it sounds like when used in some sentences), for instance:
John: "Are we going yet?"
Amy: "This will take just a bit." (says this while putting on her eyeshadow)
John: (looking at Amy while she continues to put on her mascara, her lipstick, her blush on..)
John: "How many more minutes?" (sounding impatient)
Amy: (while putting on more face powder) "Just a litttle bit more, honey."
And finally, after an hour...
Amy: Honey, come on, wake up. We'll be late.