
So, they are inserting a leap second at the end of the year. What this means is that after 23:59:59 comes 23:59:60 then 00:00:00. Traditionally, "10!" happens at 23:59:50 down to "1!" at 23:59:59 then "Happy New Year!" at 00:00:00.
The Times Square ball drop and the Atlanta peach drop are both taking the leap second into account, starting the verbal countdown of "10!" at 23:59:51, so the masses will likely be counting accurately. Unfortunately, many people will be counting according to their own clocks, or under-informed news stations' clocks. A number of ways to resolve this problem present themselves, some more disruptive than others depending on whose clock you are watching.
When Bob says "10!" ... "Happy" "New Year!" you say "11!" ... "1!" "Happy New Year!". Or start at "10!" when Bob says "9!", producing effectively the same results. This approach puts you out of sync for the entire countdown, and will likely produce the most strange looks.
Count down "10!" to "1!" with Bob, then when he says "Happy" "New Year!" you say "Leap!" "Happy New Year!". The synchronized countdown will avoid confusion, but "Leap!" should still be obvious.
Change Bob's clock ahead of time, putting him one second off until midnight* but adjusting the countdown and "Happy New Year!" to the appropriate time.
* - Technically the leap second is at 11:59:60 GMT, so it happens in the early evening for us Americans, but convention dictates that it is inserted at 11:59:60 local time to avoid timekeeping confusion for daytime applications. If your job involves timekeeping with physical clocks and computers that do GMT/UTC conversion, this is something you should already be aware of.