What are you really looking for here...even if it is in writing it still means nothing. Nothing you will get in writing will be enforceable.
They could say "Bonus up to 5 billion dollars based on company performance, merit, 100% within the discretion of senior management" and it is still worth nothing.
For the record...my company includes bonus targets in offer and retention letters...but they are meaningless.
It comes down to this ...do you feel good about the people there or not? Because the written details of a discretionary bonus isn't worth the paper it's printed on.