You don't need a public folder to make this work at all.
Set the permissions on the mailbox so that you can create a MAPI profile, and use Outlook to open the mailbox. I've got OL2000, if you have a different flavour the options might be different, but look for Tools -> Options, Calendar Options button, Resource Scheduling. This has a tick box to "automatically accept meeting requests and process cancellations". When you tick that, you get 2 more tick options available, "automatically decline conflicting meeting requests" and "automatically decline recurring meeting requests" (we usually tick the first two and leave the last unticked).
Also on the same screen is a "set permissions..." button, this is a shortcut to the Properties of the Calendar folder. CLick the Permissions tab, and set a suitable permission for the group of people you want to be able to access the calendar - for instance, if you want everyone to be able to create bookings for the room, but not fiddle with other people's bookings, then a Default of Author will do. If you want to restrict bookings to a group of people (say a department), use a DL to grant the Author permission, and leave the default at None or Reviewer.
That's it. It should then function exactly as you wish.