If I have to, I'll probably create a "project" where I log the billing, but if there's something more appropriate I would like to use that. It would be good to be able to see how many unbilled hours there are for the next billing cycle. For strapped clients, I also need to be able to do a partial billing where some work is performed, but not billed until later.
Also, I noticed that when I set up the logger to log both time and expenses, the project pages seem to always go to expenses, and the time entries are invisible, except when I attempt to add another time entry. Let me know if this is not clear and I'll submit a real bug report.