If, as has been suggested, William Shakespeare adapted his play The Merchant of Venice from that of his prematurely-deceased contemporary Christopher Marlowe’s The Jew of Malta (also known more formally as The Famous Tragedy of the Rich Jew of Malta), then the answer to the question—why did Antonio and Bassanio approach Shylock for the loan rather than some other moneylender—lies in “the Bard’s” fealty to his source material.
Both Shakespeare and Marlowe’s plays are highly prejudicial towards Jewish people, replete with often crude stereotypes common to much of history. Historically, Jews were prevented by majority non-Jewish (often Christian) populations from serving in most professions. What little was left to Jews as a means of financial support often involved finances, including moneylending. The stereotype of the Jew as pernicious moneylender, then, took root and found its literary apotheosis in Shakespeare’s The Merchant of Venice. If Shakespeare, inspired by Marlowe, sought to build the dramatic half of his play (in contrast to the more comedic half, that involving the competition to win the fair Portia’s hand in marriage) around the issue of a barbaric financial arrangement, then, it was only natural that his antagonist would be a Jewish moneylender. After all, let’s look at Marlowe’s early description of his “Jew”:
“The story of a rich and famous Jew who lived in Malta: you shall find him still, in all his projects, a sound Machiavelli; and that’s his character.”
Now, could Shakespeare have had his protagonists approach a moneylender other than Shylock, who Antonio in particular views as the scum of the earth (In Act I, Scene III, Shylock verbally attacks Antonio, saying, “You call me a misbeliever, cut-throat dog, and spit upon my Jewish gabardine”)? Hypothetically, yeah, sure, but then what becomes of the play Shakespeare envisioned and adapted from that of Marlowe? Antonio and Bassanio’s dialogue makes clear that the answer to the former’s money woes, which are incurred for the benefit of the latter, lies in an arrangement with Shylock. The assumption is that Jewish moneylenders are the only option—that pernicious stereotype, again—and that Antonio will swallow his pride and arrive at an agreement with Shylock for the 3,000 ducats in exchange for a pound of his, Antonio’s, flesh should he fail to repay the loan within three months. Antonio is sufficiently confident and arrogant in his business dealings that he cannot envision a failure to repay Shylock in a timely manner. Responding to Bassanio’s reservations regarding such a barbaric arrangement, Antonio merely replies:
Why, fear not, man; I will not forfeit it:
Within these two months, that's a month before
This bond expires, I do expect return
Of thrice three times the value of this bond.
The short answer to the question regarding the source of funding for Bassanio’s plan to woo Portia is that Shylock is assumed to the be the most readily-available source of money (although Shylock himself notes that he will be borrowing the money from another party) and that Shakespeare’s narrative demands such a singular focal point for his protagonists’ ire and efforts at securing the needed money. For the purposes of the story, there was hardly need of injecting into the narrative a protracted debate about alternative sources of money, although Antonio does note early-on that he himself never charges interest.