It may be that you will have to pay for your first day's travel to the induction centre but on the first day of your induction I would be very surprised if some kind of temporary travel pass wasn't issued. Every time I was asked to go to a location when I started with my company i.e testing, medical etc, I was sent a temporary pass to cover the journey. On the first day of induction I was given a temporary card which gave me the free travel on my TOC's services.
Phone your HR and ask, they don't bite! (well mine don't)!