In the play How I Learned To Drive, Cousin Bobby, also know as B.B. for "Blue Balls," is the protagonist Li'l Bit's cousin. He has no lines in the play and is essentially a flat, static character. The reader does not know much about him other than the fact that Uncle Peck gave him a a fishing lesson when he was young, similar to the way he would give Li'l Bit driving lessons, so we can infer that he was molested as well.
We can also assume that Cousin Bobby comes from Lil Bits' mother's side of the family. First, like the rest of Li'l Bit's side of the family, he is nicknamed after genitalia: "Blue Balls." Next, because Uncle Peck has access to him, he must be from the mother's side.
There is no way, however, to determine who exactly his parents are as it is never explicitly stated, but we can infer that Aunt Mary is not his mother as this would mean that he was molested by his own father, and this is never suggested. We can, on the other hand, assume that he is the child of one of Lucy's sisters or cousins, probably a single mother since Bobby's uncle is the one to give him fishing lessons.