Here’s another small plugin I wrote: Group Invite By Email.  Basically, it adds an email field to the bottom of the usual “send-invites” screen.  Then, when you click “send invites” it sends the person a nice little email explaining they’ve been invited to your group, and giving them a link to register on your site.

Once they complete the registration, it automatically adds them to the group.  It does this by checking their email address against a list of outstanding invites.  This removes the extra hassle of needing to invite them to the group after you’ve gotten them to sign up, and them needing to approve your group invitation.

In the future, this functionality will likely be bundled with another plugin already existing: Invite Anyone. That plugin allows you to invite non-friends to your group; this one allows you to invite non-members.

Here it is:
buddypress-group-invite-email (.zip)