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
3rd party app Digested - does exactly what you need: "Quickly import bookmarks and notes from iBooks on iPhone, iPod, iPad, export to PDF and Evernote..."