Could we use the phrase " I walked my bike to home. Or I walked my bike into home. Or I pressed my bike to home. or I pushed my bike to home."? Are they correct? Which one is natural sounding? To home? Into home? Only home? Please answer to me.
The most idiomatic way to say this in American English is: I walked my bike home.
We use the phrase walk my bike to describe the action of walking while pushing or guiding a bicycle, typically by holding the handlebars with two hands, or the stem with one hand, or sometimes holding the seat (this is less common, because it's more difficult to steer).
Bicycles will typically roll easily on their own, meaning you don't have use much force to make them move forward. Thus, there's an analogy to walking my dog (you don't have to work to make your dog walk, though you may need to guide it).
I suppose this is why push my bike is less common. To me, at least, pushing implies more effort than walking. I might use push my bike to describe moving a motorcycle (but this may not be correct - motorcycle riders have their own lingo).