We verify user profiles with automation and manually. Automated user profile verification is instant. When a user is rejected in automated profile verification. Users are requested to drop an email to firstname.lastname@example.org for manual verification. Manual verification might take upto 2 - 4 four days.
Keep checking your mail regularly, as your user verification team may ask you for additional information over the mail until your account is verified.
Keep in mind that you don't need to be verified to trade on bitbns. Verification is essential only when you are looking to withdraw.