Bhishma had the boon "Ichchha-Mrutyu" (one who can decide when to die). So he saw four generations of his family. I just want to know, what was the age difference between Bhishma & Abhimanyu in the Mahabharata?
I discuss in this answer the age of various Mahabharata characters. In particular, Bhishma was 140 years old at the time of the Mahabharata war. Now as you can see in this web page, Abhimanyu was born 12 years after Yudhishthira's coronation in Indraprastha, and Yudhishthira was coronated at the age of 46. So since (as I discuss in that answer) Yudhishthira was 91 years old at the time of the Mahabharata war, Abhimanyu was 33 years old at the time of the war (contrary to the popular belief that he was 16). So Bhishma was 107 years older than Abhimanyu.
Difference should be ~70+/- years.
As discussed in this answer, Drona died at the age of 85 years. From that, we can assume that Bhishma's age should be of 85-90 years, as both Bhishma & Drona were contemporaries along with KripachArya.
Abhimanyu's age was 16 years as mentioned in Sambhava Parva:
Nara, whose companion is Narayana, will be born as Indra's son and indeed, will be known as Arjuna, the mighty son of Pandu. This boy of mine shall be his son and become a mighty car-warrior in his boyhood. And let him, ye best of immortals, stay on earth for sixteen years. And when he attaineth to his sixteenth year, the battle shall take place in which all who are born of your portions shall achieve the destruction of mighty warriors...