At the moment, it isn't possible to add a user as a billing contact only without being added as a member.
To add a member to your dashboard, you can do so through your dashboard by following these steps:
Click on Account in the top right corner of the dashboard.
Select Account Management
Select Company Members.
Choose the "Invite Company Members" option
If you feel that this particular feature is important for you, please reach out to our Customer Happiness team and they'd love to discuss it further with you.