The shift M > P is common because M and P are both bilabial sounds (made with the lips). Will > Bill is somewhat similar.
There is a theory that the B of Bob(by) was "attracted" by the B already in Robert, in the same way that Nan became a nickname for Ann.
I can't think of any other examples of an R changing to a B in a nickname, or of R > D except for Richard > Dick. But it may be true that Rs tend to change to other sounds because they are hard for foreigners (and children) to pronounce. Rs are known to change to Ls (Mary > Molly) or are dropped altogether (Margaret > Maggie).