Based on the Gemorah in Pesachim Daf 111b is there any problem for children to hang their bags with bread inside of it by a Talmud Torah?
There is no problem in hanging bread from a bag, and certainly by means of a school bag. This is “normal,” and does not indicate any disrespect for the bread.
The idea of the Gemara is not to do practices that are disrespectful to the bread, including “hanging it.” This will not apparently appy to the case of a school and so on, where no disrespect is involved.
I have seen similar rulings cited from a number of poskim.
The issue of hanging bread, whose source is in Pesachim (111b), is mentioned by a number of poskim: see Ben Ish Chai, Pinchos 2:12; Shulchan Aruch Ha-Rav, Shemiras Haguf 9; Kaf Ha-Chaim 180:14, 434:13, Yoreh De’ah 116:198; see Shemiras Ha-guf Ve-hanefesh 31:2.
Authorities permitted hanging up bread in school include: Meor Ha’Shabbos 2:30:4, p. 166 note 605 (citing from Rav Shlomo Zalman Auerbach zt”l), Eitz Hasadeh 16 note 25, adding the opinion of Rav Elyashiv, may he be healthy; Vezos Ha-Berachah p. 18 quoting from Rav Sternbuch. However, Rav Chaim Kanievesky is cited as being stringent on this matter (Tzohar 7 p. 150:14).