We purchased 6 ft bamboo planks and cork underlayment to go over a very uneven gypcrete subfloor. The contractor did a patch job with the subfloor, floated the bamboo over it, and now we're left with a floor that has a lot of gaps between the boards, squishes and creaks, and is visibly uneven. What was the problem and how can we fix it?

You already know the answer...you gave it in your title. Now, there definitely could be other reasons for the gapping but, just for confirmation, yes...squishes, creaks, visibly uneven...all point to the subfloor. Painful to hear, but your only option is to tear it out and start over where the problem lies. Put the money, time, and effort into correcting it, or roll out some carpet.