As long as you don’t mean any disrespect, it is permissible for you to put it in the bag in such situations. Of course it is best to put your bag on the table.

I wanted to ask about manners for Quran. Is it permissible or even good to keep ur Quran in ur bag in that situation when u have to keep ur bags on the floor where childrens run and play sometimes children’s feet touch the bag too.