Similar to the process for inviting sellers to sell on your marketplace, buyers will have to receive a buyer invitation to buy on your marketplace.
As an admin, you can invite buyers to your marketplace in the admin portal under Users, in the User Mgmt. tab.
Click Invite Consumer and/or Invite Merchant and type in the email address. An invitation will then be sent to them via email.
Alternatively, users may indicate their interest in selling on your marketplace by indicating their interest when they are re-directed to the private marketplace page.
You will then see their email on the Waiting List under the User Mgmt. tab in the admin portal. Should you choose to grant access to them, you are able to send them an invitation via email as well.
Once done, they will have to onboard as a buyer/seller via the invitation sent to them through email.
Here is a video link that will assist you in setting up a private marketplace.