My company ipad uses an app called airwatch, I looked it up and was amazed how much info that they can log, including all the url's of all the web page visited, jailbreak detection, GPS logging, ssid of all the networks that the ipad has been connected to, etc.
This app does not have to be running to work, even if closed in the app bar that shows when you double click the home button.
Truth be told, they probably are not going to routinely look at the web pages visited, unless their system flags something (like a website for a union drive, LOL) or they do a random audit.
No way that I know to defeat the system or erase any logs (I believe that they are uploaded to a central server.) I would just avoid more "personal business" using your companies property in the future.