When you make any change regarding your store's domain, it will take some time before you see the change reflected when you visit the domain. Because the change must be reflected in all the nameservers around the world, you may not be able to see your store while your customers may.
If you made a change to the domain settings, such as changing the name servers, the change will usually be reflected within a few hours, although it will depend on many factors and can take up to 72 hours.
A domain transfer, where BigCommerce will become the domain registrar, can take up to 14 days. Additionally, there are certain restrictions. For example, a domain cannot be transfered until it has been owned for at least 60 days. Please see this link for more information about domain transfers.
Please keep in mind that you cannot transfer your domain name if you have not owned it for 60 days. Please see the following link for the Terms of Transfer