Halacha forbids partaking of "Pat Akum," or bread baked by a gentile in his own home. Even if all the ingredients and utensils were Kosher, one may not eat bread baked by a non-Jew in his personal premises. (Shulchan Aruch, Yore Deah, siman 112:1-2)
The authorities debate the question of whether this Halacha extends to bread that a gentile bakes in a bakery. The Shulchan Aruch (ibid) brings that by "Pat Pattar" (bakery bread), there are some places that are lenient provided of course that the bread was baked under proper Kashrut supervision.
Those who follow the lenient position should nevertheless refrain from partaking of "Pat Akum" on Shabbat, particularly when fulfilling the obligation of Lechem Mishneh (using two loaves of bread at each of the three Shabbat meals) (Mishna Berura, siman 242, seif kattan 6.) Many pita houses in Brooklyn and leading brands of pita are run by gentiles, and thus even those who partake of this bread generally should refrain from doing so on Shabbat. It is perhaps for this reason that the custom developed for women to bake Chalot on Erev Shabbat, to ensure that all the bread consumed on Shabbat had been baked by a Jew.
If, however, the only bread available on Shabbat is bread that had been baked in a gentile bakery, one may and must use that bread to fulfill the obligation of partaking of bread on Shabbat.
Summary: One may not partake of bread prepared by a gentile in his home. Many people follow the view allowing the consumption of kosher bread baked in a gentile bakery, but on Shabbat one should be stringent in this regard, unless he has no access to bread baked by a Jew.
