It was an April bonus? You are quitting well before April. I would not expect, and in fact would be shocked to receive, a bonus if I quit three months prior to the bonus date, even if it was for work already performed. I mean, it can't hurt to ask and I don't fault you for that, but as you said, it's a business and that goes both ways. It's an April bonus, you won't be working there in April, so...
Language used when offering/promising the bonus also matters, if you wanted to attempt to force their hand legally.
And I think that attempting to be agreeable, without making it in to a direct quid pro quo, might have increased your chances. Your approach sounds fairly mercenary, which means you can expect mercenariness in return. Bonuses are generally intended to keep employees happy so that stick around, even if they are sold as rewards. They have no reason to want to keep you happy and you made it clear you have no loyalty to them (which is understandable), so why should they be loyal to you?
IOW, to answer you question directly, not it wasn't out of bounds but I don't think your approach made it more likely (and wouldn't be surprised if it made it less likely) they will do so.