Is it possible to CREATE EVENT to another server? I have serverA and ServerB. I need ServerA to copy a database to ServerB and UPDATE/INSERT/DELETE as it changes. I think this can be done with replication but I don't want to continually open a connection. Is it possible to use CREATE EVENT or TRIGGERS? If so, where do I start?
Replication DOES NOT require an open connection. There's even an entry in the FAQ for this.

B.13.1: Must the slave be connected to the master all the time?
No, it does not. The slave can go down or stay disconnected for hours or even days, and then reconnect and catch up on updates.

If anything, replication is the most efficient solution when you only want to send changes from a master server to a replica periodically