I lost my original reply to this, the gist of which was that I thought that, particularly in the case of Bilbo and Frodo, the passing into the west was in order to enable them to make a "good death" and was a reflection of Tolkien's Catholicism. Bilbo's life has been unnaturally stretched by the ring whereas Frodo's has effectively been shortened. They are granted a spell in Aman to find peace and reconcile themselves mentally with their unusual lives. Frodo and Bilbo both go through stages of dying that patients with a terminal prognosis go through prematurely. If you look at this list you can see several paralels:
http://www.focusonals.com/developmen...nd_of_life.htm
IE They tidy up their legal affairs, pass on their story in the form of the red book, withdraw from their circle of friends (Bilbo, initially by going to RIvendell) and have reached a level of acceptance. In a sense for them, the West is a hospice. Bilbo's I think would be short, but Frodo I think might hold on for Sam ....