I'm so sorry, that's really tough. <big hug> My second and bestest-ever cat Hecate died of CRF due to polycystic kidneys, oh, it's going on twelve years ago, now, and I still miss her.
I took Hecate's body home (do some vets seriously not let you??) and um well actually I wrapped her up and put her in the freezer for a month til I could take her to my parents' home in PA (where she visited twice yearly with me and she loved it there) and buried her there. I guess not everyone wants a dead cat in the freezer though
or even HAS somewhere to bury a pet. In which case your options are usually a pet crematorium (ka-ching!) or leave the body with the vet to be disposed of with other euthanised pets and surgical tissue and so forth. AFAIK it just goes to a landfill as medical waste type stuff? I guess it depends on your personal beliefs but to me it seems like the animal is not gonna care any more at that point, burial or cremation is more for US (if we choose) than for the animal.
One thing you could consider, if it bothers you that you were unable to bury her yourself, is to either make some sort of memorial for her to put in your garden -- I have done this for some other situations, and taken time to select a really special rock that would remind me of the individual being memorialized -- or to plant something in her honor, preferably something pretty hardy, I've planted crocus bulbs and lilac bushes as memorials. Obviously people differ, but to me, it is nice to have be able to go visit a stone or flowers sometimes.
Condolences,
Pat