For me, as in other Shakespeare comedies, it would be better to ask who the heroine is. It is Portia in this play who shines out as being the character who heroically solves the situation that the menfolk, including her new husband, are unable to even begin to resolve. It is she who is described as active, whereas her husband is left standing passively, watching his friend Antonio about to be butchered by Shylock without being able to do anything. The initiative for this stratagem comes from Portia alone, and she in every sense shows herself to be superior to the male characters of this play. During the court scene it is she who controls the action and is looked up to by everyone, including the authorities, for her superior judgement, wisdom and skill.
With such things in mind, let us consider whether Bassanio could be judged a hero of the play. Again and again, in spite of his ability to choose the correct casket and gain Portia for his wife, Bassanio is shown as a less than impressive figure. He starts off by asking his friend to get into debt for him, because he has wasted his money, so that he can gain a wife who will bring him money. He speaks of Portia being more a financial investment rather than a person whom he loves and cares for. Although we may argue that he comes to lover her during the course of the play, the initial scene where he confesses his spendthrift ways to Antonio and asks him for more money leave a very bad impression. His subsequent helplessness in the face of Shylock's wrath and fury present him as a weak character, and to my mind unfit for Portia.
So, to my mind, the true hero of this play is Portia in the way that she is able to solve the legal dispute that nobody else is able to cope with.