How long does gum disease take to develop to this level (see pic) in cats?

Your cat, your vet bills. If the breath is horrible then there's a rotten tooth in there that needs to be removed. Ask the vet also about stomatitis (something cats are prone to more than dogs) and also about feline bartonella (which is treated with antibiotics, a lot of 'bad presentations with the mouth' are feline bartonella).

It's a good case of gingivitis, but not "nasty gum disease", and we have no idea if she has bad teeth or not, not from the picture. I am not seeing the bloody red gum lesions of stomatitis, but of course this is a picture and not real life. Very few rescues or shelters have the funds to do dentals or advanced medical procedures on cats - they use what little money that they have for spay/neuter, worming, etc. Read your adoption contract - see what it says. You can also call them to discuss the policy with them. My suspicion is that they will ask you to return her. And if her breath is that bad, didn't you notice it before? A great number of cats get dumped in a shelter or surrendered to rescue because of bad teeth - people don't want to spend the money getting a cat a dental, so they get dumped and it becomes someone else's problem.

Call the rescue today and discuss this with them. Again, ultimately you will probably have the choice between returning the cat, or paying for the dental yourself.

She is now your cat and fully your responsibility get her treated now

anytime in pet's life. consult a doctor. just like us, they have vitamin deficiencies as well. you have to combine solid and semi-solid food in their daily diet.