Recent research on bidirectional heuristic search (BiHS) is based on the must-expand pairs theory (MEP theory), which describes which pairs of nodes must be expanded during the search to guarantee the optimality of solutions. A separate line of research in BiHS has proposed algorithms that use lower bounds that are derived from consistent heuristics during search. This paper links these two directions, providing a comprehensive unifying view and showing that both existing and novel algorithms can be derived from the MEP theory. An extended set of bounds is formulated, encompassing both previously discovered bounds and new ones. Finally, the bounds are empirically evaluated by their contribution to the efficiency of the search