France's Bartoli reached the second round with a 6-3, 6-3 decision over Laura Robson of Britain.
Safarova of the Czech Republic, meanwhile, was leading Varvara Lepchenko 6-3, 4-1 before the American retired with a left wrist injury.
Also notching Day 1 wins were Sloane Stephens of the United States, who dispatched Austrian Tamira Paszek, 6-3, 6-1, and Spaniard Carla Suarez Navarro, who bested Hungary's Agnes Szavay 7-6 (7-3), 6-4.
LGBT community has 'bullied the American people': Bachmann
Duggar sisters unveil Christian dating rules in new book