Thank you for posting.
It's possible to set this up on Bob's computer, but then he will also need to be able to open the file directly. This means he needs to copy the file to his computer or access it on a fileshare. If there is a copy of the database on each computer, it's possible for them to get out of sync. If the file is hosted on a remote fileshare, there can be performance or corruption issues.
The ideal solution is to host the database from a computer that is always on and leave the file open. In larger offices this would be another dedicated "server" machine running FileMaker Pro or FileMaker Server but it could be either Alice's or Bob's computer also.
Thanks for your detailed reply, TSuki.
Unfortunately, a dedicated server is not an option. I will now try to set up Bob with full privileges and sharing set to "on" and see if Alice and Bob can swap host/client roles.