Dear Ms. Hyatt,
Thank you for posting your request on History Hub!
We searched online but were unable to find any reference to the term “Cross of Bourbon,” or to the Spanish term "Cruz de Borbón" being used in any nonfictional contexts. Every article we located refers to the cross as the "Cross of Burgundy" or “Cruz de Borgoña” in Spanish. Although the House of Bourbon has been the ruling family of Spain at times, to include the current House of Borbón-Anjou, we were unable to locate examples of it being referred to by their name. Rather, it has always been named after Burgundy.
We hope this information is helpful.