We have documentation indicating that he was born in 1609, which solves some problems with his timeline: https://books.google.com/books?id=kFWBQbCMMZUC&pg=PA123&lpg...
But it seems unlikely that his parents are correct, and his daughter may not have married Thomas Witten of Maryland.
FamilySearch has a well-documented profile for his father Peter Bulkeley: https://www.familysearch.org/tree/person/details/MF7N-YHJ According to this source Peter and his wife weren't married yet in 1609, the documented date of William's birth, and William is not on the list of children. There are a few other trees on Family Search that list William as a child but say that his birthdate is 1618. No documentation though, and his mother had a different child that year who did not live long enough to reproduce. None of the other Bulkeley sons have a daughter Mary that matches William's daughter. There are some sources who say William is the brother of Peter Bulkeley not his son, but I haven't seen any documentation for this. FamilySearch doesn't show a brother named William, and indicates that the last sibling of Peter Bulkeley was born in 1585.
Wikipedia lists a son William, citing a book on the Bulkeleys as a source; but the lack of information on William suggests that he didn't live long enough to be christened. https://en.wikipedia.org/wiki/Peter_Bulkley
Mary Bulkeley (William’s alleged daughter) was married in Barbados in 1656. The rest of the Bulkeley family emigrated to Connecticut in 1635: https://www.familysearch.org/tree/person/sources/LH6W-HHX William is documented as being a landholder in Barbados in 1638: https://books.google.com/books?id=kFWBQbCMMZUC&pg=PA123&lpg... So if he actually belongs to this family, he decided not to accompany them and moved to Barbados instead.
The marriage record doesn't mention the names of Mary Bulkely's parents, but it says very clearly that her husband's name is Thomas Switter not Thomas Witten. It's possible that the clerk misunderstood the name, and based on the documents for Thomas at https://www.familysearch.org/tree/person/sources/LTTZ-YNQ it looks like the name started out as Witter and eventually ended up as Witten, possibly in a later generation.
A more likely explanation is that these aren’t the right people. According to the more complete timeline on Family Search, Mary and Thomas Witten were childless for ten years after their marriage then suddenly started cranking out lots of babies, including five that were born after Mary’s death. The one that concerns me personally is Thomas Witten, who was born during her lifetime. https://www.familysearch.org/tree/person/timeline/LH6W-HHX Some of these children were born in Connecticut (consistent with the Peter Bulkeley family) and some were born in Maryland (consistent with the Wittens).
There are christening records showing that Thomas Witter of Maryland had a wife named Mary, but there doesn’t seem to be any evidence for her maiden name or her parents’ names. FWIW Wikitree lists William Bulkeley as Mary’s father but says his parents are unknown, and that they got the information from a family tree on Ancestry: https://www.wikitree.com/wiki/Bulkeley-257
William Bulkely was apparently a prominent person in Barbados. A search for Bulkely Plantation Barbados turns up a bit of historical information, as well as the fact that the property is currently for sale for 8 million dollars, and the main house is more than 10,000 square feet. At https://www.ucl.ac.uk/lbs/estate/view/634 it says "William Bulkeley was listed as a landowner in 1638. The plantation remained in the hands of the Bulkeley family until 1724". So if he died in Virginia as claimed in his profile, he did not sell his plantation when he left Barbados. Note that William is supposed to have died in Virginia, when his parents and siblings moved to Connecticut and his daughter died in Maryland. Not geographically close to any known family membe.
At http://www.igrealty.com/property/bulkeley-great-house/ it says "This St. George property has been a home to a number of prominent Barbadian families and dates back to 1651 when Sir William Bulkeley was a member of Parliament." This probably means the Parliament of Barbados, not the English Parliament. The Barbados Parliament has existed since 1639.
I can't find any information on who his parents were, or the names of his other children. Page 57 at http://www.uwipress.com/sites/default/files/JCHVol39%231Final_with%... suggests that the head of the family in 1688 may have been Rowland Bulkeley.
