Yes, baking soda is wonderful! If you have frequent UTIs I would highly recommend Kombucha (there is a a thread about it). It's an amazing probiotic.
Also, I would not drink that much water in one sitting. Here is why... when there is liquid in the bladder, the bacteria has something to feed off of. You want your bladder empty, but you want to have the good stuff pushed through it to kill the bacteria and clean it out.
LEMONS! Drink lemon juice WITH baking soda. Gulp as much as you can in one sitting. Wait until you have to pee (it's a UTI come on now... but it will lessen

) and completely empty your bladder so there isn't anything there for the bacteria to feed on. After you've gone potty, gulp as much lemon water with baking soda as you can and wait to go potty again. This will cleanse you out, and keep the feeding ground empty so the bacteria do not multiply.
Also, I would recommend inserting 1 garlic clove (peeled) vaginally at night. It'll come out the next day... or the next... It has AMAZING antibacterial properties.
Also, I recommend staying AWAY from douches or soaps on your vagina. You do not need to clean with soaps, they have so many chemicals in them and it irritates the vagina! Your body runs with soap in showers anyway and water is fine. I recommend "blotting" the vaginal area every few days or so with a wash rag that has Witch Hazel on it. This is what's on Tucks pads. It's a natural astringent.
Some more recommendations:
Shavegrass
Also known as Horsetail. Nutritious, helps the body absobrb calcium, may help to strengthen bones, hair and nails. Control excess oil on the skin. Diuretic, helps to relieve urinary disorders. May help blood to clot, reduce fevers, and calm nervous tension.
Niaouli (Oil) - urinary infections, heals burns, antiseptic for broken blisters, sore throat, respiratory problems, aches, acne, bronchitis, dull skin, flu, whooping cough.
garlic capsules orally
1/2 tsp. of baking soda in 8oz glass of water
Vit c
Echinacea
Citrus fruit
Grapeseed Extract (GSE)
Blueberries - promote urinary tract health