Users can update their own BSA number in Scoutbook by clicking My Dashboard > Administration > My Account > Switch SSO Profile > Enter the BSA number and their My.Scouting username and password > Update. It will then prompt them with an message that asks if they want to change their BSA number in Scoutbook. They can confirm this change.
If you run into difficulties, change your member ID in My.Scouting using the instructions here.