Gollum..

[Gordis]

Firstly, Bilbo didn't age dramatically between the time he left the Ring to Frodo (TA 3001) and the War of the Ring (3018). It was only after the Ring was destroyed that he has aged very fast.

Arwen: "For you know the power of that thing which is now destroyed; and all that was done by that power is now passing away. But your kinsman possessed this thing longer than you. He is ancient in years now, according to his kind; and he awaits you, for he will not again make any long journey save one."-LOTR, Many partings.

I think it was like that. Bilbo was 50 when he got the Ring. He remained the same age (physically) until 3001, then started to age again. So by 3018 he was 50+17=67 years old physically. With the Ring destroyed, he became 111+17=128 years old all of a sudden, which is very old for a hobbit.

As for Gollum, let us say he was 17 in TA 2463, when he got the Ring. He was physically still 17 when he lost it in 2941. He started to age normally, so by 3018 he was 17+77= 94 - old, but still fit and quite well adapted to the life in the wilderness. However he knew that with the Ring destroyed he would "turn into dust" (becoming suddenly 573 years old and thus dead.)

And skip spence is right, in addition there might have been some lingering effects of the ring, making those who had it once age at a slower rate afterwards.