I can understand your worries -DD1 was only 4 when she first used school transport and it is unsettling until there is a routine in place.
It's excellent that you will have a regular driver.If you ever have a replacement,check the licence card and ensure that the school know to do the same.
Speak to the school.Establish with them exactly what will happen after school.For example,will your child go to the office,and will an office staff member take him out to the taxi,or will the taxi driver come and fetch him.Establish that the school will ring and let you know if the taxi is late,so you don't worry.Swap your own home number and mobile with the taxi driver - hopefully the taxi driver will give you their own number too.
Ensure that child locks will be used. Quickly glance around the taxi at first and establish that you are happy that the state of the taxi and that any debris has been removed that you would not be happy being in the back of the taxi with your child.
Establish what will happen when your child arrives at the school - it is likely that the taxi driver will take your child to the school office. Ensure there will be an actual handover between adults.
It will be fine,and asking loads of questions and understanding the safeguards the school and taxi will have in place will help you settle with it much better.
There is no harm in ringing the school at first just to make sure your DS has arrived happily at school!
I have found that the vast majority of drivers are dads,and really look after the little ones.