I haven't heard about your relatives because my bernardi's relatives- that I have identified- lived in PR in the eighteenth and nineteenth centuries.However, they have to be related to your family because I found their information in the parish microfilms of Aibonito and Cayey.
Antonio Bernardi was married to Maria Alberti had a daughter by the name Andrea Bernardi Alberti. Andrea was the greatgrandmother of my grandfather.They were from the municipality of Cayey and probably from a ward that later became the municipality of Aibonito.It seems that Antonio and Maria were not originally from Puerto Rico but I havent found more information. Once my father told me, he knew someone by the last name bernardi.If you want to talk more about how I obtained this information email me.I hope we can exchange some information. Ismael.