My grandmother (Marion Ardis Bullis) is a descendant of Philip, her line being: George Washington Bullis, William Charles Bullis. Milo J. Bullis, Thomas Bullis, Thomas Bullis, John Bullis, Thomas Bullis, and finally Philip Bullis and Judith Hart.
I once posed the same question and got back the following "informed" opinions. I guess you can pick the one that seems to suit.
1. "The Bullis family originally came to England in 1066 from Normandy with William The Conqueror (William I). The name is from the French "Bois Ville", or village in the woods". (This was from "Personal and Family Names", Harry Alfred Long, published in 1883, London, England by Adams and Company.
2. BULA: meaning bull. The name Bool thru Bulpin are derived from this old English word. The names Bullas, Bullass, Bullus, and Bullis, are simply modern contractions or simplifications of the term: Bull-House. (Reference was anonymous)
3. BULLIS: Cattle Tenders. (This was published in "English Ancestral Names - The Evolution of the Surname From Medieval Occupations", J.R. Dulan.
4. BULLIS: Originally spelled Bullace, referring to a type of wild plum, growing along hedgerows in England. The fruit is used in the production of slow gin. (Reference was anonymous)
Variations of the name that I have thusfar found include, but are certainly not limited to: Bulis, Bulliss, Bullice, Bullace, Bullus, Bollis, Bulles, Bolles, Boulis, and Bullas.
Have fun ... I basically gave up on trying to find an authorive answer to that question (but I lean heavily to the Norman line, coming to England ... as are many Irish or Scottish surnames derived)