Bus

The bus drives relatively slowly (making pursuit fairly easy) between a set of locations on the map. If left alone or kept at a distance, all of its passengers will get out and go to the location of interest, taking pictures of it with bright flash photography. Why they do this is uncertain, but it is likely they are documenting something or trying to find out what has happened to the world.

If the player has their headlights and/or drive too close, the bus will evade them. If the passengers are disembarked when this happens, they will rapidly board the bus before it takes off. They are not hostile, but clearly highly secretive.

The Spider Child will show the player a photograph of him and the Hazmat Child together, and if the two tail the bus and keep their distance when it parks, the Hazmat Child will break away from the group and come join the Spider Child in the player's vehicle. The bus passengers make no attempt to stop this or to get him back afterward, making it unlikely that he was kidnapped for any reason but rather was found on the loose and they wanted to keep him safe.

Story
The bus somehow came into contact with the Hazmat Child, and either kidnapped him or took him aboard to keep him safe.

Motives of passengers
In a recent update, they are described as "tourists" which explains their interest with certain locations where they are taking pictures.

A possible theory for the current state of the world of Beware is that a nuclear disaster occurred, which could explain their clothing being to protect from left-over radiation or irradiated particles in the air. If a pandemic was a cause of the disaster instead, this could also explain such measures as masks and full-body suits being worn to prevent catching the sickness.

Trivia

 * The bus is the largest vehicle currently in the game. However, in the v008 Demo, the large, autonomous dump trucks absolutely demolish the bus in size.