In most English speaking countries it's a far from common phrase (ie. it's very USA-centric).
Maybe you don't have "hospital bills". I don't have "landscaping bills", but I know exactly what they are.
As you've pointed out, the word "bills" clarifies what it is. I don't see why every combination needs to be in a dictionary. The list would be incredibly long, eg. "phone bills" or "power bills", etc.