I woke up around ten, I made cup of coffee, and took it into THE bedroom
Is using 'the' correct in this sentence?
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.”