It says that when he found the ring he stops aging, but when does he continue to age? When Bilbo leaves the Shire in TA 3001 or after the One Ring is destroyed in TA 3019
I don't think he stopped aging as much as it slowed down the physical effects of his aging. Even with the Ring, or perhaps because of it, he felt its mental effects. He probably aged visibly after the Ring's destruction. There's no way of knowing how long he lived after sailing West, but I doubt he lived for many years. He was probably dead by the time Sam sailed to Valinor.
In the films, at least, it is apparent that Bilbo has not completely stopped ageing. Even in the books, I doubt that he looked exactly the same at age 1111 as he did at age 50 when he found the Ring. But I would say that the effects of the One Ring started to fade immediately after he gave it up and left it for Frodo. Certainly it was noticeable when Frodo saw Bilbo again after reaching Rivendell.
I don't think he stopped aging as much as it slowed down the physical effects of his aging. Even with the Ring, or perhaps because of it, he felt its mental effects. He probably aged visibly after the Ring's destruction. There's no way of knowing how long he lived after sailing West, but I doubt he lived for many years. He was probably dead by the time Sam sailed to Valinor.
In the films, at least, it is apparent that Bilbo has not completely stopped ageing. Even in the books, I doubt that he looked exactly the same at age 1111 as he did at age 50 when he found the Ring. But I would say that the effects of the One Ring started to fade immediately after he gave it up and left it for Frodo. Certainly it was noticeable when Frodo saw Bilbo again after reaching Rivendell.