Must one wash on bread by the Erev Tishe Beav meal or/and Seudas Hamafsekes?
The large meal: There is no requirement to wash on bread for the large meal that is customarily eaten prior to Mincha and each person is to eat whatever he sees fit so he be satiated and not be harmed by the fast whether it be bread or another starch.
The Seudas Hamafsekes: Although we do not find any recorded requirement to wash on bread for the Seudas Hamafsekes, it is nonetheless proper to do so, and so was the ancient custom from Talmudic times as recorded in the Rishonim and Poskim, and therefore so should be followed. Either way, whether one eats bread or does not eat bread, it remains forbidden to eat more than one cooked food by this meal [i.e. any cooked food other than the cooked egg].
 See Nitei Gavriel 51 footnote 29 that in Vizhnitz their custom is to eat mezonos and not hamotzi for this meal. To note that in truth there is no requirement at all to eat a last meal, and hence certainly there is no requirement to eat bread. [See Nitei Gavriel 51:4 footnote 6] Nonetheless, since the custom is to eat a big meal after midday with more than one cooked dish and possibly fish, therefore one must eat one more meal later on in order so has previous meal not be considered the last meal which contained these restrictions which were not followed.
 Betzel Hachochmah 4:55; Nitei Gavriel 51:8; See Or Letziyon 3 p. 244 in gloss that it is not only proper to do so but is an actual requirement
The reason: Aside from the fact that this is the old age tradition, it is proper to do so in order to make this meal be truly considered the Seudas Hamfsekes meal which contains the restrictions of eating more than one cooked food. If this meal were not to be defined as a true meal then these restrictions would have applied to the previous meal eaten after midday, in which many partake in more than one cooked food. [Betzel Hachochma ibid]
 See Michaber 552:6 that those who are able should only eat bread with salt [the cold hardboiled egg ] and drink water during this meal; Rama 552:6 that many are stringent to conclude their meal by dipping their bread in ash and then eating it; Taanis 30 regarding Rav Yehuda Bar Ilaiy that he would eat black bread; Yerushalmi Taanis 4:6 that Rav would eat bread dipped in ash and say that this is the meal of Tishe Beav; Midrash Raba Eicha 3:6; Brought in: Ramban in Toras Hadam p. 248; Rokeiah 310; Ravayah 3:888; Or Zarua 2:515; Sefer Hamanhig Hilhos Tishe Beav 24; Shibulei Haleket 265; Orchos Chaim Hilchos Tishe Beav 8; Hagahos Maimanis Taanis 5 Pei; Beis Yosef 552
 Betzel Hachochmah 4:55; Nitei Gavriel 52:4