How can one atone for the sin of avoiding paying bus fares and unintentionally taking school supplies, knowing that the buses belong to the state and it is difficult to identify their owners?

As for the bus fare, the amount of which you do not know, you must investigate its amount until you are reasonably certain that you have fulfilled it. Then, exert your effort to find out the authority to which the buses belong, so you can return the money to them. If you are unable, then give it as charity to the poor among the Muslims, because money whose owner is unknown is spent for the benefit of Muslims, and charity is one of the greatest of these benefits.

As for the tools, it is most likely that they are insignificant items that their owner would not pursue, or things that are discarded because they are unwanted. Therefore, there is no harm in taking them and benefiting from them.

As for what becomes mixed up for you, causing you to take something that is not yours, if it is not something discarded or an insignificant lost item, then you are obliged to return what you took to its owner if you know him. Otherwise, give it as charity on his behalf. We advise you to sincerely repent and regret what has passed, and to hasten to do good deeds, for "indeed, good deeds do away with ill deeds."