Office 365 Exchange Online users cannot book conference rooms that resides in Exchange Server 2003 server on-premise in Hybrid deployment.
The issue occurs because Auto Accept Agent is not installed.
To work around the issue, move the resource mailbox to Exchange Server 2010 mailbox server.
Note: The Auto Accept Agent is configured by default in Exchange Server 2010.
Understanding Auto Accept Agent
Exchange 2003 Auto Accept Agent vs. direct booking
Office 365 Exchange Online