Liquor laws may differ where you are but I wouldn't recommend bringing alcohol into a bar where I live. If you're caught, you'll, at best, be kicked out.
I’m not advocating ripping off the bar. But if you and whoever you may be with are already in $100 range, I think it’s fine to do. They markup the prices pretty dramatically and it makes a difference if you are going out a lot.
Until anyone has run a bar, I don’t think they understand much about the industry’s finances. There are many costs that don’t appear obvious at first.