Wordpress Sites Hacked - Looking for a Solution

I recently had several WP sites hacked - the hackers splash screen is attached.

The hacks were across several sites from WP3.7 to WP3.5 and I could not find a pattern of plugins. A malware check showed several 404.php theme pages were compromised, and one of the sites was running BulletProof Security.

As I have several sites, (100+), is there a fairly easily managed solution to prevent hackers from gaining access?

Thanks for your advice!