What is the ruling on praying Fajr in the bus weekly for someone who fears missing work, or praying it at home and being late for work?

You are not Islamically prohibited from riding the bus before the time for Fajr begins. If the time for Fajr begins, ask the driver to stop so you can pray. If he refuses and you are able to get off and catch another car, then do so. If it is difficult for you to get off and you know that you will be delayed or harmed, then you are excused for praying on the bus, as Ibn Taymiyyah mentioned that obligatory prayers are valid on a riding animal for fear of being cut off or harmed. The Permanent Committee also mentioned the permissibility of praying on the bus according to one's ability if the prayers cannot be combined and the bus will not stop until after the time has expired. It is better for your faith to look for a solution, such as praying at home before going to study.