It is unlikely. Ringworm is a fungal infection, that is spread by skin to skin contact and sometimes via surface contact, such as wrestling mats. If she had clothing on over the rash, she can not spread it through the clothing to the seat. If the area of the rash was in direct contact with the seat, you can clean it off and/or don't immediately sit there with exposed skin. Once she is treated, she is not contagious.