Hello @ArtSal, if that first set of JSON is everything returned from the asset-bundle, you are missing a lot more than just sheets. It looks like it just has the dataset information. I am assuming it is because you are missing the exact permissions for the AssetBundle APIs.
"quicksight:DescribeAssetBundleExportJob",
"quicksight:ListAssetBundleExportJobs",
"quicksight:StartAssetBundleExportJob"
Also, make sure you specify the asset-bundle resource:
"Resource": "arn:aws:quicksight:*:*:asset-bundle-export-job/*"
I believe those updates should resolve the issue, but make sure to inspect the analysis definition in the bundle to see if the sheets array contains the proper JSON for the analysis. Let me know if this helps!