What is the ruling on eating beef that the country imports via smuggling and bribery?

There is no sin on you for buying beef in your country and
eating it, even if smuggling is widespread, for the following reasons: 

Firstly: 

The basic principle is that it is permissible to eat meat
that is sold in Muslim markets without asking or enquiring into its origin
and source, on the grounds that what appears to be the case is that the meat
is being sold in a permissible manner in a legitimate marketplace; so the
Muslim should not concern himself with asking questions or examining
details. The Mother of the Believers ‘Aa’ishah (may Allah be pleased with
her) narrated that some people said: O Messenger of Allah, some people bring
meat to us and we do not know whether they mentioned the name of Allah over
it or not. The Messenger of Allah (blessings and peace of Allah be upon him)
said: “Say the name of Allah over it and eat it.”

Narrated by Muslim in his Saheeh (2057). 

Al-Haafiz Ibn Hajar (may Allah have mercy on him) said: 

We learn from this that everything that is found in the
markets of the Muslims may be taken as legitimate.

End quote from Fath al-Baari (9/635). 

Ibn al-Qayyim (may Allah have mercy on him) said: 

(The scholars) were unanimously agreed that it is permissible
to buy meat without asking for proof that it is halaal, being content with
the word of the slaughterer and the seller.

End quote from I‘laam al-Muwaqqi‘een (2/181) 

Secondly: 

If we assume that there is something wrong, it only affects
the one who is doing the smuggling and breaking the law. As for the buyer
himself, he is not committing any sin or doing anything wrong, and he is not
helping in any sin or transgression. Allah, may He be glorified and exalted,
says (interpretation of the meaning):

“No person earns
any (sin) except against himself (only), and no bearer of burdens shall bear
the burden of another. Then unto your Lord is your return, so He will tell
you that wherein you have been differing”

[al-An‘aam 6:164]. 

Thirdly: 

Beef that has been slaughtered properly is halaal meat
according to the consensus of the fuqaha’, and it does not become haraam if
it reaches the country by illegal means. The prohibition [on smuggling] does
not apply to the meat itself, contrary to the case if the cow is slaughtered
in a way that is not prescribed in Islam, such as if the name of Allah is
not mentioned over it or it is slaughtered in a manner other than that used
by the Muslims. In that case its meat is haraam. As for smuggling, the
prohibition does not make the meat haraam; rather the wrongdoing in this
case is limited to breaking the law of the land. 

Fourthly: 

The fact that the people would suffer a great deal of
hardship if a fatwa were to be issued forbidding them to buy this meat is
sufficient evidence that it is permissible. According to what is mentioned
in the question, the vast majority of the meat that is sold in the
marketplaces comes from the smuggling mentioned. Moreover, there would be a
huge rise in prices if this source of meat was banned. The basic shar‘i
principle on which there is scholarly consensus says that hardship makes it
permissible to be lax in implementing shar‘i rules. 

To sum up:

Regardless of the laws of these countries and whether they
allow the importing of cattle or not, and regardless of the extent to which
that serves the interests of the people or not, none of that has any impact
on the meat of these cattle, even if the consumer is certain that it comes
from smuggled cattle. 

And Allah knows best.