Question: Is it necessary to leave bread on the table during Birkat Hamazon?
Answer: The Tosafot in Masechet Berachot (42a) write that their custom was to take care not to remove the bread from the table until after Birkat Hamazon. Several other Rishonim write likewise.
This means that at the conclusion of the meal, one should not clear the entire table, including the tablecloth with whatever bread remains on it, and then recite Birkat Hamazon; rather, the tablecloth and bread should be left on the table until after Birkat Hamazon. Indeed, Maran Ha’Shulchan Aruch (Chapter 180, Section 1) writes: “The tablecloth and bread should not be removed until after Birkat Hamazon.”
The reason why the bread should be left on the table until after Birkat Hamazon is discussed by the holy Zohar (quoted by the Kaf Ha’Chaim, ibid, Section 1) and states that blessing can only take effect when there is something there for the blessing to rest upon. We find similarly in the book of Melachim regarding Elisha the prophet who told the wife of Ovadia the prophet that an abundance of blessing would rest on the small amount of oil she had in her possession; however, he did not perform a miracle that something should emerge from nothing. This is because it is easier to extend the effects of the blessing from something which is already existent than to create something from nothing. The tablecloth and bread must therefore be on the table while one is reciting Birkat Hamazon so that one may extend great blessing and abundance upon himself.
There is a more simplistic reason for leaving the bread on the table during Birkat Hamazon quoted by the Levush which is that we do so in order for it to be noticeable that we are blessing Hashem for His kindness and goodness by sustaining all of His creations.
According to the great Mekubalim, one should likewise take care not to remove the salt from the table until after Birkat Hamazon. This opinion is quoted by the Sefer Halacha Berura (Chapter 180, page 272). We have already discussed the words of the Poskim regarding this law in a different Halacha.
Summary: At the conclusion of the meal, one should leave the tablecloth and whatever bread remains on it on the table until after Birkat Hamazon. According to the Mekubalim, the same holds true regarding the salt.