Is there a way to export my highlighted bookmarks in iBooks? I don't see any native functionality to export highlighted notes made from within iBooks

Is there a third-party tool that will allow this?
yes there is, if you have a mac.

Get iExplorer here
http://www.macroplant.com/iexplorer/

plug in your iOS device and use iExplorer to
look in the books file and drag the following files to your desktop.
iBooks.plist  and iBooksData2.plist

and this app
https://github.com/lgoss007/BookmarkExtractor

put the files in the appropriate spot and you can get your highlights