I try to avoid going a lot longer than necessary without water, so I don't go off road where there is no water to filter for more than two days. If it gets to the point where I will need to carry three or more days of water whether for bike touring, bikepacking, or backpacking, I start to rethink the trip.

That said I have fairly often had to go a full 24 hours or a little more with no water resupply. For me that is generally only a day here or there on a longer trip.

Given my usage... I find that it makes sense to have two bottles on the frame maybe a small bladder. Additional capacity is added in the form of scrounged sport drink or bottled water bottles. I add capacity as needed and discard as soon as it is not needed. I carry the extra either in my baggage, in a little backpack (either my 2.5 oz s2s or my 12 oz Flash 18), or even in jersey pockets. I try to use the water stored in the least comfortable places first, so when I had a gallon of water in jersey pockets I used that up first.

That all has worked well for me since even on a coast to coast trip there would be only a few days where water wasn't available at least once during the day, even on the Southern Tier.