As a cuckold whose wife loves bareback sex with her lovers, I am very aware that this could happen any day. My wife is on the pill, but she does not hide her fantasy of getting pregnant from one of her bulls.
I think the easiest way to go with it is to tell everyone it came from a sperm donor and that we both agreed with it (which it is actually true). Her best friends know about our lifestyle though, so it would not work for everyone.
Showing her more love than ever and assuming my role rising the baby, would make it work.
A cuckold has to understand his wife's needs and getting pregnant by one of her bulls is a very natural one.