Yeah, sop up the wetness first, and then spray white vinegar until completely saturated. You can even pour it on the stain and let it penetrate the mattress. You can do this and keep soaking up with a towel to kind of 'flush out' the urine. The vinegar not only neutralizes urine smell, it kills the bacteria and prevents it from making mildew and mold within your mattress.
You can even flush the stain with some hydrogen peroxide or OxiClean. Hydrogen peroxide may bleach out the fabric of the mattress, but you can probably dilute it or use OxiClean without any problems. I just use vinegar alone.
When dry, you can put some more baking soda - rub it in, and then vacuum.
I have a dog that has seizures and since he's a big dog, in the past, if he was on my bed and had a seizure he'd make a big mess. The vinegar and baking soda combination definitely works. There's no stain either.