Her paternal aunt puts her money in a riba-based bank; can she accept her hospitality?

Firstly: 

If your aunt has another, permissible source of income, such as a salary from permissible employment, there is no sin on you if you eat her food and accept her hospitality, because what the scholars have stated is that if a person’s wealth is a mixture of halaal and haraam, and they cannot be told apart, it is permissible to interact with him, buying and selling, lending and borrowing, etc. It is also permissible to eat his food. The Prophet (peace and blessings of Allaah be upon him) and his companions interacted with the Jews, and they ate their food, although their wealth was not free of haraam elements, because they took riba and consumed the people’s wealth unlawfully. 

But some scholars say that wealth which is acquired via riba is haraam only to the one who acquires it, and there is no sin on the one who takes it from him in a permissible manner, such as if it is given as a gift or offered in hospitality. 

Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) said: 

Some of the scholars said: If something is haraam because of the manner in which it was acquired, the sin is only on the one who acquired it, and not on the one who takes it in a permissible manner from the one who acquired it, unlike that which is haraam in and of itself, such as alcohol and goods confiscated by force, etc. This is a strong argument, based on the evidence that the Messenger (peace and blessings of Allaah be upon him) bought some food for his family from a Jew, and he ate from the sheep that was given to him by the Jewish woman in Khaybar, and he accepted the invitation of a Jew, although it is known that most of the Jews deal in riba and consume haraam wealth. End quote from al-Qawl al-Mufeed ‘ala Kitaab al-Tawheed (3/112). 

He also said: As for that which is haraam because of the way in which it is acquired, such as that which is acquired by way of deceit, riba, lying, and so on, it is haraam for the one who acquires it, but it is not haraam for others, if they acquire it in a permissible way. This is indicated by the fact that the Prophet (peace and blessings of Allaah be upon him) used to interact with the Jews even though they used to consume haraam wealth and take riba. That indicates that it is not haraam for anyone other than the one who acquires it. End quote from Tafseer Soorat al-Baqarah (1/198). 

But if your refusal to accept this hospitality will affect your aunt and make her repent from this haraam action, then undoubtedly it is more appropriate for you to refuse this hospitality. 

And Allaah knows best.