Where I work, we use Bugzilla extensively for bug and feature tracking. We take advantage of the built in milestones to help us manage our timelines better, but sometimes priorities shift and milestones need to be rearranged. During this time we use the "change several bugs at once" feature to move them around, but the result is a ton of bugspam for everyone involved (except the person actually doing the changing, of course).
Is there any way to easily turn off emails if many bugs are being changed at once?
Yes, but it requires administrator access. In the Administration section, go to Parameters : Email : mail_delivery_method and set it to Test (to spool emails to a file on disk) or None (to completely disable email). Then, make your change and re-enable your email. You may want to put a message in announcehtml so any other users using the system will know that no emails will be going out while you are changing your bugs.
You could also convince your users (and/or set the default options) to deselect the option in the Email Preferences that sends email when "The priority, status, severity, or milestone changes."