Yes, the Ring continued to extend Bilbo and Gollum's lives after they stopped bearing it up until the destruction of the Ring.
Gandalf himself alludes to this when talking about Bilbo:
it might take a long while for the influence to wear off. ... he might
live on for years, quite happily: just stop as he was when he parted
Since neither Gollum nor Bilbo appear to age significantly after losing the Ring, despite their already extended ages, that's a reasonable assumption.
Bilbo had deteriorated significantly by the time he left Middle Earth, which concurs with this conclusion. The Ring had been destroyed by then so any legacy effect it had on him would have ended. Arwen would have only left Rivendell a few weeks after the Ring was destroyed to travel to Minas Tirith, but when she got there she commented
Do you wonder at that, Ring-bearer? 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 ... is ancient in years now,
according to his kind; and ... he will not again make any long journey
Obviously the destruction of the Ring was already having the effect that Gollum also alluded to when he said
when Precious goes we’ll die, yes, die into the dust.
We never got to witness this because of his encounter with the interior of Mount Doom instead.