No - there is no fermentation time for non alcoholic ginger beer.
Pretty much mix all the ingredients and pour into the bottle! This is because there is no need to convert the sugar to alcohol which is what the fermentation process is for.
The only time there is need for some level of 'fermentation' is once in the bottle. This is with the addition of sugar is the process to carbonate the ginger beer and get it nice and fizzy.