on a bike

[Ashiuhto]

Which of the following sentences acceptable?

1. On Cindy's way back home, two kids on a bike ran into her.
2. On Cindy'w way home, two kids riding a bike together hit her.

[JMurray]

Both of your examples suggest that the two kids were riding the same bike, like a tandem. Is this what you mean?

Or do you mean that they were each riding their own bike?
If so, then: "On Cindy's way back home, two kids riding bikes ran into her".

not a teacher

[Ashiuhto]

Yes, what I mean is the two kids were riding the same bike.

[JMurray]

Yes, what I mean is the two kids were riding the same bike.

A bike that two people can ride together is called a "tandem bike/bicycle", or simply a "tandem".
So: "On Cindy's way back home, two kids on/riding a tandem (bike) ran into her".

not a teacher

[JMurray]

It occurs to me, Ashiuto, that you might mean a bicycle that is made for only one person, but a second person is riding on the bar, handle bar or on the back. This has got various names in different parts of the world. In Australia it's often called "dink(s)", and "to dink".
"Can I have a dink over to John's house later?".
"Peter dinked his younger brother all the way home".
In New Zealand when I was a kid we always called it "doubling" or "dub(s)".
"My tyre's gone flat, can you give me a dub home?"

So for your example, if you don't mean a tandem bike then you would normally use whatever the local term is for two people riding a single-person bike.

not a teacher

[5jj]

In Australia it's often called "dink(s)", and "to dink".
"Can I have a dink over to John's house later?".
"Peter dinked his younger brother all the way home".
In New Zealand when I was a kid we always called it "doubling" or "dub(s)".
"My tyre's gone flat, can you give me a dub home?"

Interesting.

This speaker of BrE has never encountered these terms.

[Tdol]

Neither have I and I don't know what the terms would be in BrE.

[bhaisahab]

Neither have I and I don't know what the terms would be in BrE.

I've heard "Can you give me a bar?" meaning a ride on the crossbar. (This was many, many years ago.)