Sponges help. So does high quality soap. I have a lot of Sponges at my place and don’t use them often, because I have good water pressure and whatnot, but they’re there in case. Also, you should have some backup water storage in case you ever lose water completely. First day you can probably go without bathing/showering completely, but can still wash your hands with 2 little sets of water. Your primary water storage can be bottled water from some place like Walmart or whatever. Those last several months or so in storage/a closet easy. I have used the water from these during short water outages to wash my hands and once even to give myself a sponge bath.
For secondary, more long-term storage, I like to use these.
They’re expensive, but will last a very very long time. You can use an equivalent brand of you find a better deal from a reputable source. Just don’t cheap out too much. Good ones that won’t leak and do their job right are kinda expensive regardless. I have them stored away from sunlight and with the prescribed amount of water extender (literally just a few drops of bleach per gallon), so the water within will be safe to drink for 5 years. Also, be sure you rinse the containers pit several times first, and have filters and purification tabs on hand at home just in case as well. This sounds expensive, but I actually live on the bottom 10 or 15% income bracket in my country. Overall, I’ve probably only spent $140 - $180 in initial investment on water prepping and just another $5 to $10 per year in bottled water to replace the bottles that I use from time to time.
My old roommate moved to Houston, Texas and then was stuck without water or electricity for several days when the snowstorm hit and they were stuck in a very dark place and had to melt snow to use for water because they didn’t have the level of preps I do on hand. And the guy she moved in with makes a 6 figure income. Seems like a cool guy, but it’s kinda embarrassing he was out-prepped by someone who makes about $11,000 a year and doesn’t live in a hurricane zone.
Obviously, if you’re new to prepping then you should also stock up on heat and light sources, food, money, gear/rugged-living clothing, knives, tools, self-defense, etc. But water is generally number 1 for most situations.
Remember the rule of 3s. You can survive 3 weeks without food, 3 days without water, 3 hours in a harsh environment (death valley heat or Iowa winter cold without the right protection), and 3 minutes without oxygen.