Bilbo frequently thinks about being home. What do those times have in common?

Hey, I’m not sure what you mean In common with? He does think about being back in the quiet shire. These memories are comforting to him, especially when he is being singed by dragon fire or attacked by orks. The memories of the simple, predictable and boring life of a Hobbit bring him comfort.

Bilbo most often wishes he were home when he's uncommonly tired or hungry, in trouble, or when contemplating a problem. Home is quiet, life is going on without him, and he feels that the people (well?) and things going one around him are completely unreasonable.

Quotes (Just a few)

"You said sitting on doorstep and thinking would be my job, not to mention getting inside, so I am sitting and thinking.” But I am afraid he was not thinking much of the job, but of what lay beyond the blue distance, the quiet Western Land and the Hill and his hobbit-hole under it."

"Bilbo was sitting [with] ... the Elvenking and Bard. A hobbit in elvish armor, partly wrapped in an old blanket, was something new to them. “Really you know,” Bilbo was saying in his best business manner, “things are impossible. Personally I am tired of the whole affair. I wish I was back in the West in my own home, where folk are more reasonable..."

"...he sat himself down with his back to a tree, and not for the last time fell to thinking of his far-distant hobbit-hole with its beautiful pantries. He was deep in thoughts of bacon and eggs and toast and butter when he felt something touch him … like a strong sticky string..."