From:
John Leach's Encyclopedia of Postal Authorities :

B

BA/BMA Issues - Belarus
Belgian Congo - Bremen
Britain - British Zone
Brunei - Byelorussia

BA/BMA Issues - Belarus

BA/BMA Issues
BA Eritrea
BA Somalia
BA Tripolitania
Baden
Baden (French Zone)
Baghdad (British Occupation)
Bahamas
Bahawalpur
Bahrain
Baluchistan
Bamra
Banat Bacska (Rumanian Occupation)
Bangkok (British Post Office)
Bangladesh
Baranya (Serbian Occupation)
Barbados
Barbuda
Barwani
Bashahr
Basle
Basutoland
Batum (British Occupation)
Bavaria
Bechuanaland
Bechuanaland Protectorate
Beirut
Beirut (British Post Office)
Beirut (French Post Office)
Beirut (Russian Post Office)
Belarus

Belgian Congo - Bremen

Belgian Congo
Belgian Occupation Issues
Belgium
Belgium (German Occupation)
Belize
Belorussia
Benadir
Benghazi (Italian Post Office)
Benin
Benin (French Colony)
Bequia
Bergedorf
Berlin-Brandenburg (Russian Zone)
Bermuda
Bessarabia
Beyrouth
Bhopal
Bhor
Bhutan
Biafra
Bijawar
BMA
Bohemia & Moravia
Bohmen und Mahren
Boka Kotorska
Bolivar
Bolivia
Bophutatswana
Borneo
Bosnia & Herzegovina
Bosnia & Herzegovina (Austro-Hungarian Empire)
Bosnia & Herzegovina (Provincial Issues)
Bosnia & Herzegovina (Yugoslav Regional Issues)
Bosnian Serb Republic
Botswana
Bouvet Island
Boyaca
Brazil
Bremen

Britain - British Zone

Britain
British Administration Issues
British Antarctic Territory
British Bechuanaland
British Central Africa
British Columbia
British Columbia & Vancouver Island
British Commonwealth Occupation of Japan
British Consular Mail
British East Africa
British East Africa Company
British Field Office in Salonika
British Forces in Egypt
British Guiana
British Honduras
British Indian Ocean Territory
British Levant
British Middle East Forces
British Military Administration Issues (BMA)
British New Guinea
British Occupation Issues
British Occupation of Italian Colonies
British Postal Agencies in Eastern Arabia
British Post Offices Abroad
British Post Offices in the Turkish Empire
British Regional Issues
British Solomon Islands
British Somaliland
British South Africa Company
British Virgin Islands
British Zone

Brunei - Byelorussia

Brunei
Brunei (Japanese Occupation)
Brunswick
Buenos Aires
Bukovina
Bulgaria
Bulgarian Occupation Issues
Bulgarian Territories
Bundi
Burkina Faso
Burma
Burma (Japanese Occupation)
Burundi
Bushire (British Occupation)
Bussahir
Byelorussia