  We study in a general way the construction of string bit Hamiltonians which
are supersymmetric, We construct several quadratic and quartic polynomials in
string bit creation and annihilation operators ${\bar\phi}^A_{a_1\cdots a_n}$,
${\phi}^A_{a_1\cdots a_n}$,which commute with the supersymmetry generators
$Q^a$. Among these operators are ones with the spinor tensor structure required
to provide the lightcone worldsheet vertex insertion factors needed to give the
correct interactions for the IIB superstring, whenever a closed string
separates into two closed strings or two closed strings join into one.
