He could not get a Hajj visa for his mother except by paying money to the official
Question

I am in a European country, and I want to take my mother for Hajj from here, because in our own Arab country, who goes for Hajj is determined by a lottery system. But in order to obtain the visa for my mother from the Saudi embassy, I was asked to pay 300 euros because my mother is not resident in this European country. This money does not go to the embassy’s coffers, rather it goes to the official in the embassy so that he will process the visa for my mother. Is this money regarded as a bribe or as a payment in return for his services?.
Praise be to Allah.If this money is given to the official, and it does not go to the coffers of the embassy, then it is a bribe and a haram gift, and the official is taking it unlawfully and it is haram for him. But if you cannot get the visa without paying this money to him, then there is nothing wrong with it, in sha Allah, and the sin is on him. 
The fuqaha’ made an exception from haram bribes in the case of that which a person pays to get what is rightfully his, and in that case it is haram to take it but not to give it. 
Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said:  
If he gives him a gift to make him refrain from wronging him or so that he will give him his due, then this gift is haram for the one who takes it, but it is permissible for the one who gives it to give it to him. The Prophet (peace and blessings of Allah be upon him) said: “I give one of them a gift and he goes out holding it under his arm as if it is fire.” It was said: “Why do you give things to them?” He said: “They insist on asking me, and Allah insists that I should not be stingy.”  
From al-Fatawa al-Kubra, 4/174.  
Taqiy al-Deen al-Subki (may Allah have mercy on him) said:   
What is meant by the (haram) bribe that we have mentioned is that which is given to avoid paying one’s dues or to get something to which one is not entitled. But if a person gives it in order to get what is rightfully his, then the prohibition applies to the one who takes it. If the one who gives it cannot get his rights except by giving it, then it is permissible, but if he is able to get his rights without it, then it is not permissible. This is the ruling on what is given to obtain positions: it is haram for the one who takes it in all cases, but with regard to the one who gives it, it depends on the situation, as we have mentioned. 
Fatawa al-Subki, 1/204  
For more information please see question no. 72268. 
And Allah knows best.