How Long Does it Take to Get to Valinor?

[Galadriel55]

Originally Posted by Puddleglum

As such, someone traversing Ilmen on the straight-way to Valinor (if so gifted to find that path) would still experience the passage of time (be it short or long). Just as they would continue to experience the passage of time after arriving at Eressea (or Valinor beyond).

Yes, time goes on and affects the traveler. However, the traveller would not feel the time. I suppose that Valinor is similar to Lorien in this sense, except even stronger. Sam didn't want to believe that he spent a whole month in Lorien, because he didn't feel the time pass by. Even though Frodo and Bilbo would eventually die in Valinor, they wouldn't really be aware/concious of the years that go by.
I don't think that it was a different plane of existence, but existence would seem to be on a different plane for, I guess, everyone except for Elves. They are used to having time pass by, since they live for millenia. And even for Elves life in Valinor would be different. The fundamental principles of "existence" would remain the same, but existence would be different.
This is all a lot of guesswork, though - existence or not. I guess it's really up to the reader to decide how far/close Valinor became. According to me it is farther, because it is beyond the "circles of the world", but on the other hand, it's closer, because you don't need to travel for weeks to get there, but you need the Valar's permission to go on the straight way. Again, this is a very debatable topic. For me the removal of Valinor from Arda was more a sybolic event than one that could change the plot significantly. When it comes to symbols, everyone has a different interpretation.