How many times is Timothy mentioned in the Bible?

Nine.

27 times in total. The KJV translates the Greek word for Timothy (Timotheos) 18 times as 'Timotheus', and 9 times as 'Timothy'. Most other versions simply use the name Timothy.

////////// The above stats include one of the names in the endings of the letters and one that is not. To be consistent with the endings Timotheos is used 19 times, without the endings the number is 17 times. King James Statistics are at the link (not case sensitive) Timotheus (17) Timothy (9)