Eileen Christina "Bibi" Zillmer (born December 15, 1952) is a former competitive figure skater who represented West Germany for most of her career. She is a three-time (1969–71) national champion and competed at the 1968 Winter Olympics in Grenoble, France; Zillmer placed 12th in compulsory figures, 23rd in free skating, and 19th overall. She finished in the top ten at four ISU Championships – 1969 Worlds in Colorado Springs, Colorado, USA; 1969 Europeans in Garmisch-Partenkirchen, West Germany; 1970 Europeans in Leningrad, Soviet Union; and 1971 Europeans in Zürich, Switzerland.