He sleeps rough in the book world out of consideration for his hosts, but it's kind of cheating that he can summon an entire giant tiger for a bed. I imagine in a city setting where you can't easily hide a tiger he wouldn't have that option, but if he could still fly he could get himself off the ground and find shelter on parts of buildings most people wouldn't see. Without that ability, or without motivation to take care of himself, he'd mope around in dark alleys. I think more than a comfy bed he wanted Byakko to talk to in the book world, as someone who knows him and makes sense to him, so it's not necessarily that he wanted to be comfortable. He's immortal and doesn't have to think about his own survival which makes an excuse to let himself suffer.
I've imagined him as a number of animals over the years but his author definitely chose dog. A Japanese spitz. His stupid clingy behaviour would translate as jumping up at people's legs and rolling around on the floor yipping and whining. He wouldn't have a sensible plan to explain who he is. Just a plan to be sticky, because he must have some purpose to have come here, and he wouldn't drop it that easily.
I wonder, if he were a bird or something would he try to gesture like having hands, or carry things in his beak. Pick something up and go tapptappatappa with it to point things out. I don't think he'd have that fine control as a dog.
Would any of it work is the question. If an animal came up to me and was very attached I wouldn't jump straight to it being a fictional character, even though I associate the breed of dog with him. But I think if he showed a degree of sentient intent, like protecting me, I'd be inclined to make a comparison and that would be his chance to react. Bark louder if you're a confused dead guy, jump if you love pie, now spin in a circle and tell me how Gensoukai arc ends. No? Well, worth a shot.