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

Sorry, but (at least currently) there's no way to do this.

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..."

You can do this on a per-book basis from within iBooks:

1. Open the book
2. Press the "list button" to bring up the Table of Contents
3. Switch to the Notes tab
4. Press the Share button
5. Select Edit Notes
6. Select All
7. Share via email or some other app.

See this other question for how to do it on macOS.