Jamwes,

In-setting, it could be that Qui-Gon knew that the parts required for that class of ship (it was a luxury vessel after all) were fairly rare, and that Mos Espa was relatively small; it'd be akin to shopping for replacement engine parts for a high-performance sports car in a sleepy Northeastern US village with a population of less than a 100 hundred people; a truly exceptional mechanic might be able to jury-rig something to get to a larger population center, but such mechanics are pretty rare, and doing so with the Queen's ship would leave them in much the same situation as they were already in.

And for all we know, he did shop around, and what Watto said about being the only person with the parts in stock was true, requiring him to deal with the Toydarian after all. Of course, not long after Anakin came chasing after Qui-Gon and was willing to help the older Jedi, at which Qui-Gon probably figured it'd be less hassle to win the parts via the podrace, particularly since Naboo was under occupation and the Queen's people were being held in what amounted to concentration camps. To say nothing of constantly asking around for parts for a Nubian vessel would increase the chance of the news reaching the wrong ears and the Trade Federation being alerted that the Queen was stranded on a hick planet and thus a prime target for re-acquisition by the TF's leadership.