To a large extent, it depends on the local environment. In places that are snowy, muddy, or sandy, people are more likely to expect guests to not wear shoes past the mud room. But in places where shoes stay reasonably clean, people are less likely to ask guests to remove shoes.

I have never heard of anyone wearing shoes in bed. That's super weird. Which movies show that?

This indeed is how Hollywood popularly depicted Americans, as wearing shoes to bed, in the bathtub or shower, while swimming, and so on. There's the famous line the the Humphrey Bogart / Katherine Hepburn film "A Time To Stand" where the robbers tell Bogie they're going to clean him out, and he says "you can take anything you want, but you're not getting my shoes!"

There was an episode of This American Life where they delved into Hollywood's preoccupation with people never (ever) taking off their shoes, and one of the things they go into is how Johnston & Murphy (old shoe company) was one of the biggest funders of the original Silver Age studios. It was maybe the first instance of product placement, right up there with cigarettes. Of course Congress eventually got involved in the late 50s and pushed the shoe industry out, paving the way for movies like George Pal's "The Time Machine" which scandalously showed Yvette Mimiuex's bare feet. The French were laughing at us, though, with directors life Truffaut and Godard already showing casual barefootedness in their experimental shorts ("La Pantoufle Perdue" being the best-known and most influential).