Moving from one train or bus to another is called "transferring":
I think we need to get off here and transfer to the 104.
The word "transfer" means to move from one place to another. A few other ways that you can use this word are:
To "be transferred" by an employer means to be sent to work in an office in a different area.
My dad got transferred overseas when I was seven years old, so I spent a few years living in Singapore and Indonesia.
To "transfer (something)" means to move it from one place to another. For example, in a recipe:
Add potatoes and cook until soft, about 12 minutes. Drain and transfer to mixing bowl.
To "transfer to (a school)" means to change from one school to another. The student who does this is called a "transfer student".
Hopefully I can take a couple of years of classes at the community college and then transfer to a four-year school.