If i exhaust my Riven, Broken Blade with my Ki Burst does Ki Burst or Riven, Broken Blade ability resolves first ?

Riven's ability resolves first. Exhausting her is the additional cost to play Ki Burst, and that happens while Ki Burst is still being played — anything that triggers during the process of playing a spell goes on the chain above it and resolves before the spell does (FAQ #4103). So Riven's "When I become exhausted" trigger finalizes and resolves, then Ki Burst resolves and Stuns its target.

So the ordering matters in your favor: you can pick the "spend my buff to ready me" mode and she'll be ready again before Ki Burst finishes — the exhaust was already paid as a cost, so readying her doesn't undo or fizzle the spell. Just note the Stun and ready modes require her to already have a buff to spend; otherwise the Buff mode is your line.

One thing to watch: Ki Burst's Stun target is chosen when you play the spell, so Riven's trigger resolving first can't change what Ki Burst is pointed at.