Non-alcoholic mint julep? Can I substitute Bourbon in this recipe? Lemonade would make it too sour. Water would make it too watery. 

I know this isn't exactly cooking per se, but the reason behind this is that I have a BUNCH of left over mint that's probably a day from going bad and I'm scrambling to
In the world of cocktails, the term for creating a drink with no alcohol is "virgin".

If you google "virgin mint julep", you will find recipes to try to simulate the beverage without bourbon.   They employ a variety of strategies, but ginger ale, lemon juice, or lemonade seem to come up fairly frequently, alone or in combination.