I discovered that the book is still available (for a pretty high price), but I'm going to see if my library can borrow it from the Library of Congress. the particulars are:
TITLE: A partial view of the Beasman-Baseman family of Maryland /
AUTHOR(S): Hiatt, Catherine C. (Main)
PUBLISHED: Baltimore : Gateway Press ; Sykesville, Md. : Orders to Fairhaven, 1986.
DESCRIPTION: 1 v. (various pagings) : ill. ; 24 cm.
NOTES: Bibliography: p. xii-xiv.
SUBJECTS: Beasman family.
Maryland--Genealogy.
LC CALL NO.: CS71.B43551986
DEWEY CLASS NO.: 929/.2/0973 ED: 19
FORMAT: Book
LCCN: 86-80676

I found used copies on bookfinder.com, but they ranged from $57 to about $80.