As they were not Spanish citizens, they did not have a second surname.
They were referred in Spain as “Principe/Princesa N de Baviera”
Even if in Spain, only the heir is Prince or Princess, foreign royals are referred as Prince or Princess.
See the case of Prince Ludwig Ferdinand of Bavaria, referred as “Principe Luis Fernando de Baviera”. https://www.boe.es/datos/pdfs/BOE//1883/091/A00001-00001.pdf
Just how exactly were his children by Infanta Amalia Filippina referred to in Spain? I know that none of them was created into an Infante/Infanta by grace there, since none settled there. However, it's common knowledge that according to the Spanish naming system, a child legally adopts both his father's and mother's surnames -- with, of course, the father's name coming first, and it being the one a son transmits to his own children.
Does this mean that all five were legally Bourbons, as well as Wittelsbachs? It goes without saying that in Bavaria, they would never have been styled with the surname Bourbon ("when in Rome, do as Romans do"). But were they ever referred to thus in Spain?
As for titles: just how exactly does the Prinz/ Prinzessin title translate into Spanish, anyway? I know that cadet members of the royal family of Spain are typically styled as Infante/Infanta; however, the heir apparent is known as the Prince of the Asturias. But none of the children of Adalbert and Amalia ever held that status.
What exactly did the Spanish press call them, if anything? The same question could apply to the next generation -- specifically, the children of Prince Ludwig Ferdinand of Bavaria and Infanta Maria de la Paz of Spain.