Bleeding in the Litterbox

Our 1 year old female cat Blossom has blood in her urine.  The vet thought she had a bladder infection and gave her some antibiotics which seemed to help a little... maybe wishful thinking because we noticed it again a couple weeks later.  She got some stronger antibiotics after that... Now her 20 day supply of that is almost gone and she is still having the issue.  She did have x-rays which showed no stones.  The vet thinks she is probably too young for cancer (though it's not impossible) Does anyone have an idea what could be causing her problem other than infection, which would have been cleared up by the antibiotics or cancer?  We had a young dog about 6 years ago who was sick, we spent a LOT of money trying to get him well and then it turned out that there was nothing that could be done for him and we had to euthanize him anyway.   I do not want to travel the same road again.  If it could be a simple fix, I'd love to keep her.  She is a VERY sweet cat.  But I do not want to spend thousands and still be without her. It's bad enough to be heartbroken, to be in debt on top of that really stinks.

does your cat eat an all-wet diet? does she drink a lot of water? how many times does she pee a day? 

it could be stress-related. 

so, feeding all wet, using Feliway diffusers and calming treats, having 2 litter boxes for her, toys, window perch, cat tree, etc. can't hurt no matter what the cause of the bleeding. and maybe get a cat water fountain. 

It may be a urinary inflammation instad of an infection. You'd be surprised how often vets get that difference wrong. Antiobiotics won't do a thing for an inflammation. Did the vet take a urine sample to culture to check for bacteria growth? Here's some info: http://catinfo.org/?link=urinarytracthealth

Feeding more canned food with water added helps many cats with urinary issues. The urinary system (and body) needs water to work at its optimal level.

I agree with @LTS3, a culture of the urine is important for a good diagnosis as it can rule in or out an infection, and if its not an infection then other things need to be done.  An ultrasound nay help as well.