In the United States, we would usually say "get on the bus." It means the process of boarding the bus. We are standing on the sidewalk. The bus stops. We "get on the bus," i.e. we step on the steps, climb up, pay our fare, sit in a seat. We are now "on the bus" and ready to ride to work. When we get to our stop, we "get off the bus." "Get in the bus" or "get into the bus" have a slightly different meaning. It emphasizes a specific detail of whether we are just outside the bus doors, or just inside them. It would be used in a special situation. Let's say the bus is very crowded. Everybody is standing. The last person tries to climb on. They are almost inside but not quite. One foot is sticking out. The driver tries to close the doors. They close part way. The safety mechanism trips. They open again. The driver yells, "Hey! Get in the bus! Get all the way in so I can close the doors! Move to the reader people, make room for him to get in the bus!" At the next stop, someone inside the bus might yell, "Hey, please let me through so I can get out of the bus!"

In the UK we get on the bus.

Get into the bus

get _into_ the bus

Get on the bus