In Exchange 2013, Public Folders are moved into mailboxes and out of their own database. Looks like the easiest way is to look at the msExchRecipientTypeDetails attribute.
search.Filter = "(msExchRecipientTypeDetails=68719476736)"
Combine that with your other search criteria.
Running a Get-Mailbox -PublicFolder on the mailbox will show the RecipientTypeDetails listed as PublicFolderMailbox. 68719476736 is the bitwise identifier that matches on the user attributes.