This option should be set to a list of options X=>v with X denoting the constant as an indeterminant and v as it's value.
i1 : R=QQ[z,a,b,c] o1 = R o1 : PolynomialRing
i2 : makeB'InputFile(storeBM2Files, BertiniInputConfiguration=>{MPType=>2}, AffVariableGroup=>{{z}}, B'Constants=>{a=>2,b=>3+2*ii,c=>3/2}, B'Polynomials=>{a*z^2+b*z+c});
The object B'Constants is a symbol.