There is a cooldown on promotions at River Rat. I believe it's something like 14 days since you became a Senior Server? So you need to work for that amount of time before you can get the bartender promotion
When you clock out of work, the text on the screen will give you an idea if you are close to a promotion or not. If you are, it will say something like you need to work a couple more shifts. If you are not close, it will say you need to work several more shifts before you can be promoted.
