Is there a quote in The Merchant of Venice that explains how much Bassanio is in love with Portia or his feelings towards her?
Your best bet for this question is to re-read III.ii. Bassanio talks a lot about Portia's beauty and wealth to Antonio and his buddies, but he confesses deeper feelings to Portia directly when he tries to win her by guessing the right casket.
First, when Portia nervously asks him to delay choosing the casket, saying if he fails it will break her heart, he says that he wants to choose quickly because he's so nervous about it (III.ii.24-5).
Then, during some word play where Bassanio compares himself to a tortured prisoner, Portia says that she will set him free if he will confess his crime, and he says
Confess and love
Had been the very sum of my confession.
It's a short, sweet, and playful answer. He's essentially telling her "all I can say is that I love you".
Portia responds that if he really loves her, then he will choose the right casket ("If you do love me, you will find me out")--and he does choose the right casket, the one with her portrait in it.
When he wins her, he describes himself as "giddy in spirit".
Maybe the most moving declaration of his feelings, though, comes when she commits herself to him and gives him her ring. Then, he says:
Madam, you have bereft me of all words.Only my blood speaks to you in my veins.And there is such confusion in my powers[...]Where every something, being blent together,Turns to a wild of nothing, save of joy,Expressed and not expressed.