You are correct that you've seen the B.D. initials before. They are listed on William Thomas' death certificate. However, I have an original copy of William Thomas' baptism and it is very clear that the father is Rufus Benjamin.
You have the names of Ada's children correct. Walter's birth date is 24 Jun 1897.
I have found that a B.D. Gullette is apparantly buried in Hillcrest cemetery in Van Zandt county. So I've still got some work to do on this. Kinds stinks that the 1890 census is gone. Sure would help.