Order of operations is a bit odd here, but not impossible. Bit of Luck applies to all d20 rolls for one round, while Elemental Focus (Mythic) causes you to roll twice for a save.
I think the correct interpretation is that the spell asks for a saving throw, rather than a d20 roll, so Elemental Focus (Mythic) applies first -- the target must roll twice for the saving throw, and take the lowest. At this point, the target is rolling d20s, so Bit of Luck applies now -- the target rolls twice for each attempt at the saving throw, taking the highest.
So:
The target will roll twice and then take the highest.
The target will roll another two times and again take the highest.
Of the two rolls selected, the target then chooses the lowest and uses that as his save.