I have created a new directory using my Microsoft account and then made it a default directory for one of my subscription. I created 2 test users under this directory - Admin(made it co-administrator for the subscription) and Bob- Global Administrator. Now the admin has access to the subcription however Bob does not have access the subscription linked with the directory. As i understand the users should have access to the subscription under the directory by default. Please correct me if wrong.
I don't believe that's correct. The subscription and directory are two different things, as the directory is a child of the subscription. So someone can be a Global Admin in the directory, but that doesn't mean that they have access to the subscription. I have however seen an option in the subscription that grants Global Admins to also have access to the subscription. This page might help: https://docs.microsoft.com/en-us/azure/billing/billing-add-change-azure-subscription-administrator