Yes, this is correct. The word “bedroom” in this sense is referring to an actual thing, and must be preceded by “the.” In fact, I can’t think of an instance when “bedroom” wouldn’t take an article. :)

In your example, “cup of coffee” also needs an article. In this case, it would be “a cup of coffee.”

Yes, this is correct. The word “bedroom” in this sense is referring to an actual thing, and must be preceded by “the.” In fact, I can’t think of an instance when “bedroom” wouldn’t take some kind of a determiner, such as that bedroom, our bedroom, a bedroom, etc.

In your example, “cup of coffee” also needs an article. In this case, it would be “a cup of coffee.”