By 1651, Paul Busey was settled in the Province of Maryland, Calvert County. To pay for the long voyage from Europe, Paul senior appears to have indentured himself to Henry Cox. The land record (5th January unknown year) is confusing,
" . . . Henry Cox Demandeth Four Hundred Acres Assigned to him by Mr. William Eltonhead (ut supra) and two Hundred Acres of Land more for Transporting himself and Paul Busey Son of Elizabeth his Former Wife into this Province Anno 1651."
So Paul was the son of Elizabeth? And did she not reach America?
As for many of the contracted immigrants, service eventually brought the privilege of land ownership. On 11 June 1659, Paul Busey (in this instance "Bucey") demanded 150 acres because of other legal provisions that he had fulfilled.
Family tradition has mentioned both Scotland and England as the origin of the Busey family in America.  There is an unconfirmed report that Robert de Buci was listed in the Domesday Book as having gone to England with William the Conqueror.  An alternative hypothesis is that Paul was a French Huguenot, a Calvinist Protestant, who was escaping the persecution of King Louis XIV, possibly by way of Holland or England.
Where did the name Busey come from? If the French connection is true, then there are a choice of names, e.g., Debussy, Dubois, and Beausse from which Busey may have derived.  Other spellings, Bussey and Bucy, are confirmed spelling variations of the Paul Busey lineage in America.  Other similar names in America, e.g., Busse, may be related.
Paul and his wife Suzanna _____, the first Busey family in the New World had two children, sons Paul (b. ca. 1660) and Charles (b. ca. 1663). Other given names among their descendants were John Busey, Sarah Busey, Susannah Busey (the daughter of Paul junior and thus named for her grandmother), Samuel Busey, Edward Busey, Joshua Busey, Anne Busey, Mary Busey,Verlinda Busey, and Clare Busey.
Unfortunately, the early Busey history is fragmented because the Calvert County Court House, and all its records, were destroyed by fire in 1882. There were several Samuel Buseys, two of whom were grandchildren of the original Paul Busey, and one apparently migrated to Rowan County, North Carolina, with his son Mathew (born 1742 near Annapolis). In 1768, Samuel Busey was one of thirty signers of a petition from Rowan and Orange counties to the House of Representatives under King George III, asking for tax relief, and other matters such as relief from tyranny and oppression of certain offices.