Would a musician born in Toledo, ca. 950, expect to travel back and forth between Arab, Frankish, Basque, and "Spanish" land?
We don't have much in the way of records for any musicians from this era (early middle ages), let alone itinerant musicians. There are a couple of mentions of musician/poet/bard at Anglo-Saxon and late Carolingian courts in the 10th century, but none suggest travelling. In fact, the trope of an itinerant musician of the middle ages probably needs some deconstruction, but I won't labour that much here. Suffice it to say that all musicians in the middle ages seem to be combined in public imagination: wandering from castle to town to pub singing alone or in groups.
In attempting to answer the question, I do want to address the poet-musicians for whom we have the earliest robust records: the troubadours (f. trobairitz). These troubadours, whose appearance between early 12th and 13th century has been described as a "brief but intense flash of lightening, crossing the horizons of European cultures, marking them forever." They provided the role models for northern French trouvères, the German Minnesänger, equivalents in Italy and Hispania, and the stereotype of romantic and cynical minstrel in general.
The troubadour, however, was not a wanderer. Many troubadours were higher or lower nobility, and if they weren't they were attached to a noble court. It is true that some troubadours were quite well travelled, and in fact some had taken up positions or visited courts in Aragon and Catalonia at times. Troubadours have a induced reputation for traveling because:
But they were not wandering musicians.
One of the biggest questions in historiography of the troubadours is of origins: where did this troubadour poetry suddenly come from? There are a number of theories, and among them is exposure to Hispano-Arabic/Andalusian song forms. A lot of ink has been, and continues to be spilled on this, in an attempt to prove a connection...which has thus far proven elusive. The short paper Arabic Influence on the Troubadours^1 neatly summarizes the four places the research arguments are made from:
A single defining moment of contact and transfer: In this case Duke William IX of Aquitaine (d. 1126, aka Guilhèm de Peitieus ) is 'patient zero', his are the first troubadour works we have extant, and he is said to have been exposed repeatedly to Arabic artistic influences in travel and battle, and through prisoners his father took captive. Most of this is rejected for evidence, and also rejected for bad history - 'patient zero' origins for cultural movements ignore genesis and transformation over time.
Formal influence: a number of historians have tried to assign the structural innovations in troubadour poetry to Arabic sources through comparative formalism. In fact formalist comparison reveals more consistent, closer links to Latin poetic predecessors, among others.
Argument from transmission through proximity: because of geographic continuity of some sort between Occitania -> North Spain -> Andalusia, there must have been transmission. This falls apart because we do not find intermediary Spanish poetic forms where this argument would suggest they should be: in northern Spain (Aragon and Catalonia)
Linguistics: some try to argue for Arabic words showing up in troubadour vocabulary. This has been inconclusive due to lack of sources for thorough etymologic connection and so it rests on conjecture. Moreover, as the author points out, their are few historians who know Old Occitan and Arabic, and it leaves a wide gap to cross.
Gorton reflects on the 'impasse' in research into Arabic origins, and 30 years later we still have the same impasse.
For getting into the history and poetry of troubadours, the best places to start are these works below; the first discusses Arabic influence in some detail:
F. R. P. Akehurst and Judith M. Davis, eds., A Handbook of the Troubadours, (University of California Press, 1995)
Simon Gaunt and Sarah Kay, eds., The Troubadours: An Introduction, (Cambridge University Press, 1999)
A more generic introduction to music in the middles ages:
^1 Gorton, T. J. “Arabic Influence on the Troubadours: Documents and Directions.” Journal of Arabic Literature 5 (1974): 11–16 . This article lists most of the useful papers which discuss the Arabic origins.