This is a scene of extremes for Bassanio. On the one hand, it is the scene where he wins his love, Portia, by guessing which casket contains her portrait; on the other, he learns that his friend Antonio has suffered a horrible setback in business and likely will be unable to repay the debt he owes Shylock, one that he took on as a favor to Bassanio.
Bassanio delivers several major speeches. His first has to do with his choice of caskets. In this speech, he says that one cannot judge the contents of a casket by its external appearance; for this reason, he is suspicious of the two gaudily decorated caskets and prefers the simple lead one. He talks (rather sententiously) about how external ornament can hide inner vice, while the music playing while he chooses suggests the right casket. So, while the process of choosing seems momentous, Bassanio's speech is an example the very thing he is criticizing. It is a very gallant speech meant to cover the fact that he has inside knowledge about which casket to choose.
Bassanio's second speech, in praise of the portrait contained in the casket, is similarly excessive. Captivated by the painting, he goes on and on about the skill of the painter, comparing the rendering of Portia' hair to a spider web meant to ensnare the viewer, or exulting over the way her eyes were painting, and wondering how the painter, having painted on eye, could resist Portia's' charms enough to paint the second. The hyperbolic nature of his speech suggests that Bassanio is perhaps a little giddy, either at winning Portia, or in outsmarting the casket game. It's hard to assign him any ulterior motive, however, so he comes off as at best besotted, and at worst, a bit vain.
Bassanio's happiness is immediately checked by the arrival of news of Antonio's bad luck and financial ruin. Realizing that his friend stands to lose his life because of his desire to win Portia, Bassanio swings abruptly from extreme happiness to extreme sorrow and remorse, and explains to Portia his debt to Antonio, and the terrible price Shylock will extract from Antonia if he is unable to repay the debt.
These mood swings characterize Bassanio as essentially good-hearted, but perhaps a bit of a fool.