I have heard over and over again from people that it's "good mazal" when a bird defecates on you. Is there any source to support this or is it entirely superstition? If it has no source, where might the superstition come from?
It has no source in Jewish literature as far as I know. The superstition is actually of Turkish origin (at least according to here). It's possible that the superstition made its way into Jewish culture, as the Turks have historically ruled over areas with high Sephardic Jewish populations. (They even ruled over the land of Israel for four hundred years; see this article from the Jewish Encyclopedia.) Although I can't say for sure that this is reason you've heard it, it might be interesting to note that it's not uncommon for a Sephardic superstition to have its origins in Muslim or Turkish culture. (Similarly, Ashkenazic superstitions often have roots in Northern/Eastern European culture.) For instance, the hamsa is a popular amulet among many Sephardic Jews, however its origins are not Jewish at all, and it is shared throughout many Middle Eastern and North African cultures.
Although I'm tempted to write more on superstition and being superstitious in Judaism (including many famous writers who cautioned people not to be so superstitious), that's not what the question was and therefore I will refrain.