It depends on how the public calendar is set up. Is it a shared calendar in an individual's account? Is it a calendar in an Exchange public folder or an Exchange resource mailbox?

If you have access to create the appointment in the public calendar, the easiest thing would probably be to create the appointment there and add yourself as an attendee. Then you will only need to accept the appointment invite for your own calendar. Otherwise it will probably require some sort of acceptance in the public calendar.

-SW