Short scale basses might seem like the logical suggestion, but kids younger than 10 learn on a full size piano without any trouble. There are plenty of YouTube videos of kids playing full size P basses, because a full size bass is easy to play, even with small hands, if you have the right technique. I'd suggest your 10 year old tries out some basses and chooses his own, but starting the same week you sign him up for one-to-one lessons so that he learns to play it correctly.