I'm not going to comment on the bug itself as no PoC has been provided (I don't think it's ethical to post it publicly without the casino's consent, anyways).
However, I wanted to salute you for your honesty and reporting the bug instead of exploiting it and milking the casino's wallets dry!
I also wanted to share my opinion on your second question:
How does someone go about reporting a bug to a casino a still hold casino accountable to pay a bounty?
You can't hold them accountable especially if they don't have a bug bounty program. Even those who have it but don't want to pay you can claim it's
a duplicate and reject your report.
That is the problem if the site doesn't have bug bounty program. You can't force them to pay or give you some reward for your work.
But if you want clear conscience, you can report it to them without waiting for any incentive.
After all, they are not forcing you to report. It is in your morality whether you report it or not.