Pedro Martínez: Sure thing, though I am not sure as to what a double room is! When I say something is with something, but not a specific thing, I always use "a". English has the two articles. "the" and "a", definite and indefinite, respectively. Your sentence sounds strange to me to just say, "double room with shower" as compared to "double room with a shower". This has me reflecting on the fact that using the indefinite article in this manner makes it very definite in the fact that it implies just one shower for the double room! :) It seems it might be better to say "double room with one shower" or "a double room with one shower" or even "a double room with shower" implying the accommodation just has one shower even though the room is double sized in other respects.

It's a trip that using the definite article to describe just having one shower doesn't seem right at all to me. I'm going to have to see if there's other instances of this. Perhaps it is a common thing and until your question I had not given it any thought.
"double room with the shower"