If this is the designated school that the Local Authority have offered your DCs a place in then, as Patchworksack says, they have a statutory duty to provide free transport to school.
Basically, the following children get free transport:-
Primary age children in Reception to Year 3 who attend their nearest suitable or designated school and live at least 2 miles from the school.
Primary age children in Year 4 to Year 6 who attend their nearest suitable or designated school and live at least 3 miles from the school; or
who attend their nearest suitable or designated school, where the parents are in receipt of the appropriate benefits, and live at least 2 miles from the school.
The distance is measured as the "shortest walking route" not a direct line as the crow flies. But if you're 6 miles away I guess that won't be an issue.
What you will need to do is to actually apply for free school transport - they won't offer it to you proactively.
So do a search for "school transport" in your area and it should give you details of how to apply.
For example, here is the form that you need to fill in where I live:-
forms.peterborough.gov.uk/356780
Hope this helps