The Book A Time interface allows you to chose among calendars that you have certain access to. In order for a calendar to show in the Book A Time interface you would need access to "Make changes to events" or "Make changes AND manage sharing". You can find information on delegating calendar access here.
Whichever calendar you chose will be the calendar that originates the calendar invite. The sender of the original email will appear as the meeting organizer, while the owner of the meeting will be the owner of the originating calendar.