I know I can't get Bermudian citizenship, but from the BritianUSA website (there were changes in 1981 but I was born in 1976 so I am not sure the more stict rule applies to me):
"The British Nationality Act 1948
3. At the Commonwealth Conference in 1947 it was agreed that each of the self-governing dominions (Canada, Australia, New Zealand, Union of South Africa, Newfoundland, India, Pakistan, Southern Rhodesia and Ceylon) would introduce separate citizenships for those persons who belonged to each country, but all would continue to share the common status of British subject, or Commonwealth citizen, both terms to have the same meaning. The United Kingdom legislation, the British Nationality Act 1948, created the status of British subject: Citizen of the United Kingdom and Colonies (BS/CUKC) for all those whose connection was with the United Kingdom itself or with a place which, on 1 January 1949, was still a colony. (This did NOT include those self-governing counties listed above).
4. The Act provided for the acquisition of BS/CUKC status by those born or naturalised in the UK or an existing colony, and by the first generation born abroad. There was no longer any restriction on the holding of dual nationality and persons acquiring citizenship of a foreign state did not automatically lose British nationality as a result. Adult aliens could acquire BS/CUKC status by naturalisation, but Commonwealth citizens and minor children were eligible in certain circumstances to acquire it by registration. Women who married CUKC husbands after 1 January 1949 had an entitlement to be registered as CUKCs themselves, subject only to the productions of evidence of a valid marriage.