Page 5 of 249 in the book "After the prophet: the epic story of the Shia-Sunni split in Islam" by Leslie Hazelton says as under:
Throughout this book, I have used first names for major
figures rather than full names, in order to avoid the “Russian
novel effect,” where English readers suffer the confusion of multiple unfamiliar names. Thus, for instance, I have used
Ali instead of Ali ibn Abu Talib, Aisha instead of Aisha bint
Abu Bakr, Omar instead of Omar ibn al-Khattab, and so on.
I have used fuller names only where there is a risk of
confusion; thus, the son of the first Caliph, Abu Bakr, is
referred to as Muhammad Abu Bakr, itself abbreviated
from Muhammad ibn Abu Bakr.
So as per this paragraph Ayesha was sister of Muhammad ibn Abu Bakr and not of First Caliph Abu Bakr.