The same phrasing is used in some areas of Canada.
We pay the hydro, we pay the electricity, we pay the phone.
Neither for nor bill is used.
Same here, it's a convenient form of shorthand. It's the kind of thing you would say, but not necessarily write.
If I say "I'll pay the gas tomorrow", the meaning is clear, that I will pay the bill of the gas company tomorrow.
(In fact, come to think of it, I would NEVER say "I'll pay for the gas tomorrow."
I'll pay for having that extra slice of cream cake tomorrow. Sorry.)