I'm not sure what you mean by "bill"?

You can link the Task to the Contact at the bottom of the Task (must be
maximised first).

You can Assign a Task to a Contact by either dragging the Contact to the
Tasks folder or making a Task and clicking the Assign button on the toolbar.
They'll get a Task Request from you in their Inbox.

You can drag the Task to the Journal for a record.

I hope one of these covers your need!

Judy