If my ten to twelve year old wasn't capable of going to the shops etc on their own I would me making sure they were.
Ds2 is ten (11 in summer) starts high school in sept where he has a walk then a bus jour ey to school, not a specific school bus just a normal public bus. He needs to be capable of doing this so going to the shops, the park, to his friends etc on his own all helps build his independence. He is very skatterbrained, easily distracted (assessed by camhs for add) but he needs to be able to do these things. And he has stepped up and taken on the responsibility well, the other day he was ten mins late home and I said to him, he has to call or be on time or he will temporarily lose the privilege of going to the park on his own.
Ds1 is 13 and at easter holidays caught the train to London (two hours from us) met up with relatives who he stayed with and then made the return journey on his own, on a recent trip to london him and his friend went of to the science museum and the others nearby whilst I and his friends mum went of to covent garden. We kept in contact by text/phone but they knew the area they were allowed to explore and stayed within it and then met up with us later in the day.
Was I nervous, hell yes but this is exactly the kind do thing he needs to be allowed to do. On school trips abroad they are allowed to go off together and he goes into our city center on his own etc. Ds2 once at high school will be wanting to go into the city with his friends, to lazer quest etc as they all do, so we have been gradually increasing his freedom and responsibilities. Letting him go to the park, walk to adn from school (40 min walk) on his own.
These things do make me nervous, my main concern would be that he gets run over by a car, abduction is not on my list of possibilities. But no matter how nervous I am, I have to have faith in him and let him become more independent, I wouldtn be doing my job as a parent if I didn't.