Sim, é permitido mover veículos da categoria A1 (!) na Espanha, se sua licença que permite que você dirija B tem pelo menos 3 anos de idade.
Cotação da Wikipedia:
B licence holders in Czech Republic (only motorcycles with automatic transmission), Italy, Latvia, Malta (after a training of 10 hours), Slovakia (after two years and only motorcycles with automatic transmission), Spain (after three years), Poland (after three years), Portugal (at least 25 years old or additional licence for mopeds), and Belgium (only with a Belgian Driving Licence, after two years) are allowed to drive motorcycles not exceeding 125 cubic centimetres (7.6 cu in) within the respective countries. In Austria (after five years, training of 6 hours), France (after two years, a training of 7 hours), Luxembourg (after two years, training of 7 hours), and the United Kingdom (Compulsory Basic Training), a practical training without exam is needed for B licence holders.
Fonte alemã: link
Wer den Führerschein Klasse B mindestens 3 anos atrás, darf automatisch a 125er fahren. Das gilt auch für Ausländer. Tradução: Quem tem uma licença da UE com pelo menos 3 anos de idade, pode conduzir motos de 125ccm. Isso também se aplica a estrangeiros.