Until 1906 this was 200th Street; sources disagree on where ‘Bedford’ comes from.
According to Bronx Community Board 7, developers built a suburban retreat of 40 homes here on farmland once owned by Leonard Jerome, and named it Bedford after the London suburb. Wikipedia instead says that the 1906 renaming of 200th Street as Bedford Park Boulevard likely honoured Edward Thomas Bedford, a Standard Oil director and associate of Jerome.