How can I model this relationship?
If an invitations is just an invitation, then it seems simplest to store all of the users for an invite in their own row in a separate table.

Users
 - UserID, PK
 - other details about the users

Invitations
 - InvitationID, PK
 - OwnerID or OwningUserID or just UserID, FK to Users
 - other details about the invitations

InvitationUsers
 - InvitationID, FK to Invitations
 - UserID FK to Users
   [PK on (InvitationID, UserID)]


A lot of people are tempted to store all of the users of an invitation in a comma-separated list or as XML. Resist this temptation; it leads to nothing but trouble.

If there is only a single type of invitation (like "be my friend on Facebook and we can hug and all that") then a simpler model might be:

Users
 - UserID, PK
 - other details about the users

Invites
 - SenderID, FK to Users(UserID)
 - RecipientID, FK to Users(UserID)
   [PK on (SenderID, RecipientID)]


If an owner can send an invitation to various things (a dating service, a boat show and a movie) then we'll need more details about what those relevant things are.