"starches are held together with A bonds, dietary fibers are held together with B bonds, and the enzymes only work to break A bonds for X reason"
What you wrote here is correct. A is primarily an α(1,4)-glycosidic bond and B in cellulose is primarily a β(1,4)-glycosidic bond.
From Chemistry of Life at abpischools.org.uk
Maltose is one of the ...