Is there a policy that can limit the growth of an AWS S3 buckets total size? We have an AWS S3 bucket that accepts uploads from untrusted sources which are then processed and moved out of the bucket. 

Is there a Policy that can limit the growth of the bucket to some predetermined upper bound to protect us in case something goes wrong?
Not as far as I know. 

You can create Billing alerts to get notifications when AWS thinks that your monthly spend may be over a given threshold.