It's weird, I breathe one side (to my left) only when sea swimming (regardless of wave direction) but perfectly happy with bilateral breathing in the pool.
I can't think of any exercises, but just slow and steady works. Focus on being consistent and don't 'gulp' air in.
I'll add:-
Are you fully exhaling under water? You shouldn't be having to exhale anything when you turn your head to breathe in.
(I've got into bad habits and it only feels "normal" to breath on one side, luckily I can maintain my usual pace breathing every 4 strokes.)