(cw: Neither of them have had top surgery)
Thorin not being able to tell Bilbo is like him in that way because of his assumed differences as a hobbit.
Bilbo, who is taking the opportunity to be around strangers and start insisting he be called Bilbo Baggins, not the name he'd been saddled with previously. (Though there is some small sadness considering he did like the name his mother gave him- but he liked Bilbo more because he and his mother had picked the name out together!)
The question of Bilbo's masculinity comes up only once. It isn't even the intention. Gloin simply mentioned Bilbo's lack of a beard. When Bilbo confirms it isn't common for hobbits of any gender, that ends the conversation.
Bilbo watches Thorin spar with Dwalin one day, a rest day after many in a row spent traveling. Dwalin is shirtless, his pale skin turning pink under the sun and his tattoos shining with sweat. Thorin is shirtless too, and Bilbo admires his broad belly and large hairy chest in small, discreet glances. It's during one grapple where Bilbo feels safe to admire openly, and his eyes widened.
Upon closer inspection, Thorin's chest does not look like Dwalin's does. The only similarity is that they both have piercings adorning them but otherwise... otherwise, Thorin's chest looks like Bilbo's.
Looking around, Bilbo saw that no one was gawking at Thorin or calling him lewd, offended at the sight of him. Bilbo had been more than once scolded and reminded to cover up as a faunt by relatives, that ladies could not show their chests like the men did no matter how horribly hot the summers got.
Truly, the only reaction received from the company was cheers and laughter when Thorin successfully bested Dwalin and pinned him in the dirt.
"That was a lucky win," Dwalin grumbled, but he still took Thorin's offered hand up.
Thorin was flushed from effort, his arm muscles defined from recent use. He flicked his hair over his shoulders as he used a spare cloth to wipe the sweat from his brow. He looked devastatingly handsome and entirely comfortable in his body in a way that make Bilbo unsure if he wanted to be Thorin or be under him.
Bilbo had to speak to Thorin. He wanted to know more, he wanted to be closer. The thought of not being alone was overpowering his fear of rejection or ridicule.
The way Thorin reacted when Bilbo got him alone said that he had expected some sort of confrontation from Bilbo.
"If you are here to try and tell me what to do or how to conduct myself, I would ask you reconsider for the sake of our friendship. I saw you looking when I sparred earlier, you disapprove?"
Bilbo was momentarily stunned, not expecting Thorin to be so defensive. "What? No. No, Thorin, I don't 'disapprove'. I-"
He hadn't told anyone before besides his mother. Telling Belladonna had been the easiest thing in the world, considering she had already guessed.
"I-" He tried again. He clutched his vest with one hand, right over his heart. "I am like you. I've never met anyone else like me, or like you."
When Bilbo dared to meet his eye, Thorin's expression had softened. Warm wonder and open kindness bloomed.
"I thought I was alone," Bilbo admitted, the weight of his heart present in those few words.
Thorin placed a hand over Bilbo's, his fingertips were rough to the touch and warmed Bilbo to the bone.
The sincerity in Thorin's voice left no room for doubt. "You are not alone. You will never have to be alone again."