The Summons

[Boromir88]

This one could go either way, I think. Radagastly brings up some good points and good quotes. And to further the argument, it could even explain why Bilbo felt a need to step out and bear the Ring to Mount Doom, as he offers in The Council of Elrond:

'Very well, very well, Master Elrond!' said Bilbo suddenly. 'Say no more! It is plain enough what you are pointing at. Bilbo the silly hobbit started this affair, and Bilbo had better finish it, or himself. I was very comfortable here, and getting on with my book. If you want to know, I am just writing an ending for it. I had thought of putting: and he lived happily ever afterwards to the end of his days. It is a good ending, and none the worse for having been used before. Now I shall have to alter that: it does not look like coming true; and anyway there will evidently have to be several more chapters, if I live to write them. It is a frightful nuisance. When ought I to start?'

Bilbo goes on about not being able to finish his book, and having thought of an ending, and being comfortable, but he just goes on with now that's all going to change. And the Ring to Bilbo is still a 'nuisance.' A 'nuisance' that he feels he has to finish.

I don't think that the Ring had a great enough power over Bilbo to make him respond to the summons. . .at least not in a way that would make him journey to Mordor!~Rune

I'd agree with this, the Ring had at this time very little power over Bilbo. Even if he held it for 60 years there are several determining factors. I'll rank them in how I feel is the most important factors in the 'corruption/influence' of the Ring.

1) The circumstances one acquires it:

Did one get the Ring after committing a crime/horrible act (Gollum) or was it out of a good purpose, as Bilbo does.

'Pity? it was Pity that stayed his hand. Pity, and Mercy: not to strike without need. And he has been well rewarded, Frodo. Be sure that he took so little hurt from the evil, and escaped in the end, because he bange his ownership of the Ring so. With Pity.'~The Shadow of the Past

2) The mindset of the Individual:

Let's take Boromir and Denethor for instance. Both were doomed from the beginning when it came to the Ring (if they should ever come across it). Boromir was full of pride, love for his country, and seeking his own glory, so before he even came across the Ring, he was doomed to fall to the Ring. This is the same case with Denethor, who never even comes close to the Ring yet he still had a desire to possess it, and saw the Ring as a 'mighty gift':

'He [Boromir] would have brought me a mighty gift.'~The Siege of Gondor

'If I had this thing now in the deep vaults of this citadel...~ibid

Hobbits weren't in this same general mindset at Men (and men who desired glory) typically were. It was Sam's 'unconquered hobbit sense' that made him endure the 'test' and give the Ring back to Frodo. Bilbo saw the Ring as an occasional trick to play, and to escape from the Sackville-Baggins', not for his further wealth, power, and glory.

3) The Knowledge of the Ring:

Bilbo didn't know much about the Ring as we are told:

..."How long have you known this?" asked Frodo at length. "And how much did Bilbo know?"
"Bilbo knew no more than he told you, I am sure," said Gandalf. "He would certainly never have passed onto you anything that he thought would be a danger, even though I promised to look after you. He thought that the ring was very beautiful, and very useful at need; and if anything was wrong or queer, it was himself. He said that it was "growing on his mind," and he was always worrying about it; but he did not suspect that the ring itself was to blame. Though he had bound that the thing needed looking after; it did not seem always of the same size or weight; it shrank or expanded in an odd way, and might suddenly slip off a finger where it had been tight."~Shadow of the Past

To Bilbo, it wasn't even the Ring that was the problem, it was himself, he never even thought the Ring was anything more than a trick and a 'beautiful thing.' And I would agree with Gandalf, that had Bilbo known fully about the Ring and what it actually was, he would never of passed it along to Frodo. Where someone like Gandalf, or even Boromir, knew more and could do more with the Ring and become even more 'terrible.'

4) Not to use a soccer term...well actually yes...but Time of Possession:

No matter what, eventually if you had the Ring long enough it would take control over you:

'Yes, sooner or later - later, if he is strong or well-meaning to begin with, but neither strength nor good purpose will last - sooner or later the dark power will devour him.'~The Shadow of the Past

Now Bilbo had had the Ring for quite a while...I would call 60 years a long time. Not like Gollum's time of possession, but still 60 years is a while. However, with all these determining factors we can see that Bilbo was still early in the corruption and hold that the Ring had over him:

"It may slip off treacherously, but its keeper never abandons it. At most he plays with the idea of handing it on to someone else's care - and that only at an early stage, when it first begins to grip. But as far as I know Bilbo alone in history has ever gone beyond playing, and really done it. He needed all my help too."~A Shadow of the Past

The Ring was still just grabbing a hold over Bilbo...I think Gandalf also makes the comment about Bilbo's use of 'thin' and 'stretched' as being a sign of the Ring's early influence over Bilbo.

So, I think it is rather a complicated question. Clearly the Ring was still at an early stage of influence over Bilbo, it was just starting to get a hold over him. Now is 'the summons' something that is only after long years and nearly full 'pull' towards the Ring, as we see with Gollum...who was nearly and fully in the Ring's power. Or is it something that happens rather early...perhaps it's just a feeling a desire one gets AFTER giving up the Ring? Because, as radagastly points out Bilbo did have this 'restlessness,' and are you one to interpret Bilbo's offer to destroy the ring as a noble and heart-filled offer...or was he feeling the 'summons' of the Ring? Or both?

One thing I'm fairly sure Rune is that 'the summons' would have to be the desire or pull towards Mordor, a drawing towards Sauron. It just doesn't make sense there would only be a 'partial summons' because what purpose would that serve? I mean to have a 'summon' that drags a past ringbearer to Rivendell...of all places...I just don't see a purpose in that situation. I would think that the summons has the specific intent on dragging the past (or maybe even present) ringbearer to Sauron, and no where else, because pulling the person to another place would really serve no purpose.