How can money be returned to the transportation company after riding without paying? Is it by informing them of what happened and paying what is due, or by purchasing a ticket of the same value without using it, or by paying a fine of 100?

You are required to pay the fare to the competent authority, and you are not required to inform them of what happened due to the general evidence for the permissibility of concealing one's own faults. Nor are you required to pay the value of the fine, because it is a discretionary punishment that is waived by repentance.