I can’t give you an answer for all of Europe, or Iberia, but I can briefly mention some work which as been done about England in the 16th century.

Miranda Kaufmann has done some very interesting work on this subject, and has studied numerous examples of black people living in Tudor England. She has surveyed a variety of historical documents, and found evidence of around 360 black people living in Britain between 1500 and 1640. They lived different types of lives, with some working as pearl divers, merchants, smallholders, or silk weavers. These black people lived both in urban centres and in more rural areas.

An interview with Kaufmann gives a good summary for how they may have arrived in England:

Black Tudors came to England through English trade with Africa; from southern Europe, where there were black (slave) populations in Spain and Portugal, the nations that were then the great colonisers; in the entourages of royals;… as merchants or aristocrats; and as the result of English privateering and raids on the Spanish empire.

Kaufmann makes the argument that black people were not completely isolated from mainstream English society in this period, before England became a major colonizing and slave trading power. She gives the examples of interracial marriages between black people and white Britons, and how black people could testify in court. I don’t know if wholly I buy the argument that black Britons would be completely accepted and integrated in more rural areas, given past research about how insular and hostile these areas were even to white British newcomers. But I do believe that they weren’t completely ostracized or outcast in this time, especially in larger urban areas where more people came and went.

So, to answer your question, it’s hard to say exactly how common black people would be in 1500s England. Kaufmann has found evidence of 360 black people over a 140 year period in Britain. This is a relatively low number, given that England alone had around 2.5 million inhabitants in 1500, and around 5.5 million in 1650. Even though Kauffmann’s figure is likely somewhat of an undercount, the real figure is unlikely to be much higher. In the late 18th century, the black population of England was estimated to be around 15,000 - and this was after centuries of England participating extensively in the slave trade and importing black slaves into Britain. So I’d say at most, there were a couple thousand black people in England in the 1500s.

On the other hand, black people did live in urban and rural areas, worked a variety of professions, and married white Britons. So they wouldn’t be completely unknown or unheard of. I feel that someone who had travelled widely across Britain would have likely met a black Briton, but someone who stayed within more remote locales (that didn’t have any black British people living there) could also never meet one in their lifetime.

See Miranda Kauffman: Black Tudors, and “‘Making the Beast with two Backs’ – Interracial Relationships in Early Modern England”.