Bonafide Resident question...

I have lived in the UK since May 2006, so I meet the Bonafide resident criteria, but I am confused what date to enter in my US tax return.

Since UK residency is greater than180 days in the UK during a UK tax year, would I have become a UK bonafide resident 181 days after my arrival in May 2006?  Should I enter this date?

You are UK resident from the date of arrival under UK domestic rules.

You also have a foreign tax home from that date, if that is your question?

The BFR date is the first date of foreign residency, which may be the same.  The physical presence test can give bonus days, so is frequently the better answer.