The base duration of the effects lasts as long as their UBB counterparts. Leveling the DBB bond level can boost their durations.
IMPORTANT NOTE: There are 2 exceptions to this: Double activation of BB/SBB/UBB effect duration can not increase more than 3 turns. Extra Action effect is also not affected.
IMPORTANT NOTE 2: Bond level 3 does not increase the effect duration of Elemental Synergy effects.