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.