If you want to keep your car looking nice while living in a Chico apartment there are more options than you think. Because of past droughts in California, many apartment complexes shut off exterior water access and removed spigots. Even if there are working exterior spigots at your Chico apartment, your parking space could be on the opposite side of the complex and running a 200 ft. hose through the middle of the parking lot isn't really an option. Here's what you can do.
Try to wash your car in the shade or under a carport and avoid the hottest part of the day. You don't want your car to dry with streaks and spots on it. Pump up your sprayers and adjust the tip so you get a good water/soap spread. Wash your car section by section working from the top down. First spray with the soapy solution and let it sit for a couple minutes and then thoroughly spray it down again before you start to scrub. Moisten your microfiber cloth with some soapy water and rub lightly, don't swirl to avoid damaging paint.
After cleaning each small section of your car you should use the rinse water sprayer to wash away the soap and dirt and then inspect for any leftover grime. It may require a second pass. Check your microfiber towel frequently, when it starts to collect a lot of dirt and grime, switch to a fresh one to avoid scratching the paint and smearing more dirt around. At the end you should take a clean dry microfiber cloth and dry the whole car, if you let it dry on it's own you will have streaks and water spots.
One of the most popular brands is the Chemical Guys EcoSmart Waterless Car Wash and Wax. A 16 oz bottle is less than $20 and makes 2 gallons of wash mixture, or about 6 - 8 car washes, depending on the size of your vehicle. If you have thick dirt and mud on your vehicle, the waterless wash isn't going to do the trick and you should probably just do a quick drive through wash to get the big stuff cleaned off. Then you can come back to your apartment for the detail work.
One of the easiest and most affordable places to get your car washed is Thorton's Chevron. If you buy at least 8 gallons of gas, you get a free basic wash which is plenty for most people. This is NOT a touchless car wash, so those of you with brand new cars and a pristine finish, this probably isn't for you. It's not perfect for everyone, but it is free, which is always the right price. Your 1998 Honda Accord with 250K miles on it will never have looked better.