So I was watching the special features of The Hobbit & it's stated that in movie canon, the song that Bofur sings in the extended edition; either he taught Bilbo or Bilbo taught him. As you can imagine my shipper heart exploded at this, haha!
Enjoy!
Bilbo was happy when he saw the village of Bree just over in the distance. It was his last chance to be with nice, polite hobbits (despite how different they were from Shire folk) before Thorin's company reached the wild. Bilbo still wasn't that happy with the dwarves over the state of his home and he wasn't happy with Gandalf either for choosing him in the first place for this bloody adventure, quest, thing or whatever.
When the company reached Bree, it was decided that they stay in The Prancing Pony for an evening, a little comfort before they were to spend countless nights on the road. Bilbo perked up at this, he had heard many tales back home about The Pony.
Once they were settled in various rooms (Bilbo was sharing with Ori and his overprotective brother, Bilbo couldn't quite exactly remember his name), the company ambled down to the pub area, ready to drink and be merry. Buying himself some ale, Bilbo made his way around the bar, stopping to chat with a group of local hobbits who had called him over. As the evening wore on and the more ale they consumed, the group of hobbits were starting to grow as merry as the dwarves, breaking out into songs and what not. Even Bilbo broke out into a song, a silly tune he made up when he was younger when he drank a little too much ale at the Green Dragon one evening.
oOo
The next morning after the dwarves and Bilbo got over their hangovers, they set out on their journey.
That evening when they stopped, Bofur approached Bilbo, "What was that song yeh were singing last night?" he asked the hobbit as he laid out his sleeping materials next to Bilbo.
"Sorry, what?" Bilbo asked, massaging his temples. Even though it was the evening, he was still feeling the effects of the previous night.
"That song yeh sung, about teh merry inn and the man in teh moon."
"Why do you want to know about that song?"
Bofur didn't answer straight away. Instead, he looked at the bowl of soup he was holding for a few moments before answering, "I would like teh learn it, if yeh wouldn't mind."
Bilbo stared at Bofur, why on earth would he want to learn that song? Not that Bilbo minded; he was quite chuffed with Bofur that he would want to learn his little song!
"Yes, you can learn it" he answered, and he felt even more proud when he saw Bofur visibly light up, "I'll write it down for you in the morning."
Bofur smiled, a smile that even made Bilbo smile in return, "Thanks Bilbo!" he said happily, clapping him on the back before continuing to eat his soup.
oOo
Bilbo looked up from his meal as he saw Bofur jump up onto a stand. Oh honestly, couldn't these dwarves just behave properly for one evening? He may have been used to their behaviour but they were at Rivendell! It shouldn't matter how much distrust the dwarves held towards the elves, the least they could do was act civil towards their hosts! Well, as civil as a dwarf could get...which was as loath as Bilbo was to admit, pretty good so far, minus Bofur jumping onto the stand. What was he standing up there for anyway? Oh goodness, he wasn't going to start throwing plates around was he?
"There's an inn, there's an inn, there's a merry old inn, beneath an old grey hill…"
Bilbo was snapped out of his thoughts as he heard Bofur sing. He couldn't really be….oh wait…yes, yes he was! Bilbo didn't know whether to be embarrassed or proud.
He watched Bofur dance atop the stand, the rest of the dwarves stomping and cheering. When Bofur finished, Bilbo caught his eye and he blinked as Bofur winked at him. As Bofur finished, he stood off the stand and approached him.
"Did yeh like it?" he asked, "I hope yeh don' mind me changing the tune and all. When I was practisin' with my flute, it was easier for me to play it that way."
"I actually think I prefer your tune better." Bilbo admitted, and he genuinely felt that way.
Bofur smiled one of those smiles again that made Bilbo smile. Maybe he should make up more songs throughout this journey, even it was for the sole purpose to have more of a chance to talk to Bofur…and to hear him sing again.
I think I might write another version but one where Bofur teaches Bilbo. Not too sure yet. But I'm learning towards it.