We can safely conclude that Bassanio is definitely not a Jew. Let us remember that at the time, Jews faced discrimination and bad treatment from Christians, as Shylock alludes to when he taunts Antonio with the power that he has over him now that Antonio needs to borrow money from him. Antonio's hatred of Jews and in particular of Shylock is evident from the text. It is therefore impossible that Antonio would have developed such a close relationship with Bassanio had he been a Jew. Let us remember what Antonio says to Bassanio in Act I scene 1:
My purse, my person, my extremest means,
Lie all unlocked to your occasions.
Therefore, to conclude, the intimacy of the relationship between Antonio and Bassanio and the way that Antonio is shown to hate Jews and in particular Shylock should lead us to conclude that there is no chance that Bassanio is a Jew and not a Christian.