The Harry Potter actor will appear in the sci-fi drama's seventh series, as first announced in February.
"He is a space pirate," Bradley told the Warwick University podcast of his character Solomon.
"We've modelled [him] on a well-known nightclub owner with long hair. He has lots of scars [and] he wears black leather."
Bradley - who has also appeared on Game of Thrones and Our Friends in the North - went on to describe Solomon as "like an old rocker".
"He... runs a ship the size of Canada," said the 70-year-old. "He has two giant robots who are a bit rusty."
Other guest stars confirmed for the next series of Doctor Who include Dame Diana Rigg (The Avengers), her daughter Rachael Stirling (Snow White and the Huntsman), Liam Cunningham (Game of Thrones), David Warner (The Omen), Jessica Raine (Call the Midwife) and Ben Browder (Farscape).
Doctor Who will return to BBC One in August.