If the tank is designed for water, and the water you put in is clean, you don't treat it. Clean water properly stored doesn't go bad. People have stored water in cisterns for thousands of years and used it without treatment.

Given that this is a rubber bladder you can expect some rubber taste, and it will be stale and flat, but it should store well enough.

There are various chemicals that will help keep it fresh, these are used on yachts where water is stored for months, but most don't make the water any safer. Some people use a carbon filter to remove the taste left from the tank, and it often helps to pour it between pitchers, letting it drop several feet to increase agitation, so oxygen lost during storage is restored and it tastes less flat and stale, but it just corrects aesthetic issues.

Traditional sailors cut their water with rum or whiskey, or, the more genteel sort, make coffee or tea with it. Some split the difference.