Shulchan Aruch, Orach Chayim, 271:9 writes:
צריך שתהיה מפה על השולחן תחת הפת ומפה אחרת פרוסה על גביו.
You need to have a table covered, under the bread, as well as over the bread. He writes his comment with regard to the laws of Kiddish. Implicit in the Shulchan Aruch is the idea that the Bread should have been brought out before you recited Kiddish, in contradistinction to the times of the Gemara when Challah would have been brought out later (see Tosfos, Pesachim 100b).
On that writes the Taz (ibid, 12):
פרוסה. בטור בשם ירושלמי שלא יראה הפת בשתו שאין מקדשין עליו אלא על היין ולפ"ז אם מקדש על הפת א"צ לכסות עליו מפה אבל לטעם אחר שכ' הטור וז"ל ואני שמעתי טעם לעשות זכר למן שהי' מונח בקופסא טל למעלה וטל למטה עכ"ל ממילא גם במקדש על הפת צריך לכסות במפה וכן אנו נוהגין:
So that the bread should not feel embarrassed because you're making a beracha on the wine first. (This should be extended as an a foritori (kol Shekein) as not embarrass people either, especially on Shabbos). There is another reason - as a remembrance for the Man that was covered with dew both below and above the Man.
However, the Gr"a argues, based on the Gemara Pesachim, 100b, Tosfos, ד״ה שאין
(see Ma'aseh Rav 118). He says not to have any challah on the Shabbos Table at all when reciting Kiddish.
The Mishnah Berura (Seif Katan 41) writes the same obligation (for those who have the Minhag to have the Challos on the table during kiddish) applies equally on Friday Night and Shabbos Day (and Seudas Shlishis - there is some discussion in the Rishonim about having wine during Seudas Shlishis also):
במפה. וכן נוהגים ומשמע בפמ"ג שלכל הטעמים די במקדש על היין שיהיה מכוסה עד אחר שגמר הקידוש וכן בשחרית צריך ג"כ להיות הפת מכוסה עד אחר הקידוש
Thus, if your minhag is to have the challah out during kiddish, then your source is the Shulchan Aruch, who brings the Tur in the name of the Yerushalmi. Then you should do so in the night and the day.
If however, your custom is to follow the Gr"a then you need not have the Challah at the table for kiddish.