They got on/get onto  the bus and went to the city.

A. onto    B. into

(1)get on骑上（马等），骑上马等；登上（公共汽车、火车等），登上公共汽车、火车等

When I got on the bus, I saw my teacher sitting there.

我一上汽车看见老师在车上坐着

(2)get onto  乘（飞机、火车，汽车等）+侧重从比较敞开的空间名词的表面通过(get onto+名词=get on to+名词)

(英文解释:When you get onto a bus, train, or plane, you enter it in order to travel somewhere.)

They get onto the plane at Cairo. 

他们在开罗上飞机.

I get onto the train every morning at 6:30. 

我每天早晨六点半上火车.

As he got on to the plane, he asked me how I was feeling. 

他上飞机时问我感觉如何。

Who can fold up a pushchair, toddler and shopping and then get them all onto the bus?  

谁有那本事一手收起婴儿推车，一手抱着刚会走路的孩子，还得提着刚买的东西，然后挤上公共汽车？

(3)get into进入；渗透进+侧重密封的空间名词/交通工具（里面/内部）（taxi/cab出租车，car小汽车）

How did the thief manage to get into the house?

这贼是怎样设法闯入屋子的？

(4)get off下去，下来；下（公共汽车、火车、飞机等），下（马等）

Never get off while the car is moving.

车在行驶时切勿下车.

(5)get out of 从…下来,后接密封的空间名词/交通工具（taxi/cab出租车，car小汽车）

We got out of the trolley bus at Yan'an Road.

我们在延安路下了电车

《麦克米伦英语词典》对onto的解释之一：into a bus, train, ship, or aircraft etc.

词典例句：

Slater was arrested for trying to carry a gun onto the plane.

The refugees were herded onto buses.

因此，显然应该说get onto the bus而不是get into the bus.