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The right to be free from unreasonable search and seizure involves government searches. The Constitution does not apply to a bartender and would not protect you.
I can think of perfectly legitimate reasons for a bartender to look into what he may have believed to be an abandoned purse. You weren't there to give or deny consent and aren't even sure how he got the bottle you shouldn't have had in your purse at all. So about the only thing you can do is complain to the management.
Again, your right against unreasonable search and seizure has only to do with government searches.
The bartender may have acted improperly -- I can't tell because despite the fact that you say there were 6 people at the table, nobody saw how he knew about or got that bottle -- but you don't have a suit here. For one thing, you didn't sustain any damages. Nobody robbed you, for example. In fact, you were even given back the contraband you should not have had in the bar in the first place.
I know that you feel bad about this, but you're not in the right either in this situation. Write a complaint to the management, as that's about all you've got here.