I have changed details on my client record in bullhorn but it is not automatically syncing to Etz?

The automatic synchronisation from Bullhorn to Etz only works on the placement being amended, all other updates needs a manual synchronisation. You can do this by going to Data Ex - Bullhorn Synchronisation. Enter the placement number the client record is associated to, then select Add item(s) to build a list of Placements you would like to manually sync. then select to Process List:-

You can also select the option "Get Current Assignments" which will re Sync all your current placements.