Sorry for not having translated your (initial) sentence: "My credit card bill has arrived."
(focus on the fact that it´s a recent thing, it´s been hours after it arrived at the moment of speaking.) (faz um 'cadinho que ele chegou.)
My credit card bill has just arrived. (agora ele "acabou de chegar).
My credit card arrived yesterday. (it´s not that recent, so we use past tense without "has".)
Sentences from the Web (here past things, not recently):
But, when the credit card bill arrived last week I casually looked at the listings and discovered we were being charged $13.77 for an Amazon bill.
When the credit card bill arrived, the acquaintance had not paid my friend, so she allowed that amount to stay on the card. This went on for several months with the business acquaintance always promising to pay. Finally my friend paid the card, realizing that this acquaintance would never repay the debt.
Source: the novel The Seven Secrets - by John Hagee.
As I pointed out, the first chunk with "last week" hints of a past (not recent one), and with the second we can see from the context around it.