Theatrics

[Arnthro]

(Gandalf)"You mean to go on with your plan then?"
"I do. I made up my mind months ago, and I haven't changed it."
"Very well. It is no good saying any more. Stick to your plan - your whole plan, mind - and I hope it will turn out for the best, for you, and for all of us."
"I hope so. Anyway I mean to enjoy myself on Thursday, and have my little joke."
"Who will laugh, I wonder?" said Gandalf, shaking his head.
"We shall see," said Bilbo.
-----(party/speech - gahwhaaaaattttt?)-----
"Hullo!" said Bilbo. "I wondered if you would turn up."
"I am glad to find you visible," replied the wizard, sitting down in a chair, "I wanted to catch you and have a few words. I suppose you feel that everything has gone off splendidly and according to plan?"
"Yes, I do," said Bilbo. "Though that flash was surprising: it quite startled me, let alone the others. A little addition of your own, I suppose?"
"It was. You have wisely kept that ring secret all these years, and it seemed to me necessary to give your guests something else that would seem to explain your sudden vanishment."
"And would spoil my joke. You are an interfering old busybody," laughed Bilbo, "but I expect you know best, as usual."
"I do - when I know anything. But I don't feel too sure about this whole affair. It has now come to the final point. You have had your joke, and alarmed or offended most of your relations, and given the whole Shire something to talk about for nine days or ninety-nine more likely. Are you going any further?"

I wonder if Bilbo and Gandalf planned Bilbo's reveal to Frodo at Rivendell. Their last little joke they will likely make together. The A Long-Expected Party joke being one of disappearing and the Many Meetings joke one of reappearing.

 

[Anthony Lawther]

(Gandalf)"You mean to go on with your plan then?"
"I do. I made up my mind months ago, and I haven't changed it."
"Very well. It is no good saying any more. Stick to your plan - your whole plan, mind - and I hope it will turn out for the best, for you, and for all of us."
"I hope so. Anyway I mean to enjoy myself on Thursday, and have my little joke."
"Who will laugh, I wonder?" said Gandalf, shaking his head.
"We shall see," said Bilbo.
-----(party/speech - gahwhaaaaattttt?)-----
"Hullo!" said Bilbo. "I wondered if you would turn up."
"I am glad to find you visible," replied the wizard, sitting down in a chair, "I wanted to catch you and have a few words. I suppose you feel that everything has gone off splendidly and according to plan?"
"Yes, I do," said Bilbo. "Though that flash was surprising: it quite startled me, let alone the others. A little addition of your own, I suppose?"
"It was. You have wisely kept that ring secret all these years, and it seemed to me necessary to give your guests something else that would seem to explain your sudden vanishment."
"And would spoil my joke. You are an interfering old busybody," laughed Bilbo, "but I expect you know best, as usual."
"I do - when I know anything. But I don't feel too sure about this whole affair. It has now come to the final point. You have had your joke, and alarmed or offended most of your relations, and given the whole Shire something to talk about for nine days or ninety-nine more likely. Are you going any further?"

I wonder if Bilbo and Gandalf planned Bilbo's reveal to Frodo at Rivendell. Their last little joke they will likely make together. The A Long-Expected Party joke being one of disappearing and the Many Meetings joke one of reappearing.

My reading of this has always been of the theatrics being Bilbo's idea with Gandalf generally disapproving, but allowing it as a means to an end: getting Bilbo to give up the ring if he can.
This happens before Gandalf's conclusion that this must be the One, but after his assessment that Bilbo's ring was a Great Ring; at least this is what he reports to Frodo in Book 1 Chapter 2.

Beyond the Three, to this point there's never been any clear evidence of Great Rings changing hands willingly except through death of the bearer and inheritance:
The ownership of the Seven is not exactly clearly detailed, merely that they were not successful in their purpose and were destroyed or recovered forcibly, and the Nine have seemingly always been under Sauron's control, suggesting that if a chosen bearer proved inferior the ring could be forcibly returned to Sauron and redistributed; there's no evidence of this happening, it just seems a logical possibility.
If Bilbo could be successfully encouraged to surrender the ring willingly to another it might be able occur multiple times. There might be hope for a plan for a millennia-long game of keep-away, or even the destruction of the ring if this proved to be the One.
If not, another plan would need to be developed, with less time available to do so.
We've seen the Wise in general, and Gandalf in particular, quite willing to play the long game, waiting nearly a century before moving against what is known to be Sauron in Dol Guldur.

Gandalf's contribution to the theatrics at the party seems to be a means to distract subsequent conversation from topics that could inform a knowing eavesdropper, like an spy of the Enemy. Even if Bilbo's ring isn't the One, no good could come of Sauron's attention being attracted to the Shire.

Regarding the "reveal" in the Hall of Fire, it certainly could have a theatrical motive, possibly even supported by Elrond and Gandalf, but it is also perfectly plausible that Bilbo just didn't have the energy to sit through the feast, and he excused himself on those grounds which is essentially what he states.
I think that a late arrival at the Feast, to the seat next to Frodo's, could be similarly theatrical, so I think we are justified in taking Bilbo at his word here.

 

[Arnthro]

Gandalf reluctantly participating makes sense.... Bilbo calls him "interfering" and I took it as Gandalf being playfully interfering with a purpose but it does seem to be strictly practical.

Furthermore your reply does motivate one to think how Gandalf would advise Bilbo with this joke if Gandalf knew it was The One Ring at that time.

**I made my post of course fully aware Gandalf wasn't certain yet.... he does not take great rings of power lightly remember so, he is still allowing the joke to occur and believes the ring is of importance and to be kept secret.