Is she straining to urinate or is there just blood in the urine but the amount coming out is normal?

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I believe if its cystitis its a bacterial infection picked up from varying sources. I've almost always seen it in females and I suspect the way they pee with the vulva hitting the ground may predispose them to picking the bug up if it is there. But talk to your vet about this too as other things like bladder stones can cause problems that look like a simple infection.
When you get more antibiotics I suggest asking your vet about a urine acidifier to use for a bit as the bacteria doesn't live well in acid urine. Or your vet may have good reasons to say no on that so ask questions and listen to the answers. I find it helpful to bring a list of questions sometimes to any doctor including the vet.
Keep up the extra fluid intake too while you do the meds.
As you are walking her on common ground let me suggest that when you get her on more meds (and you need to do that in my opinion) if you normally say go left on your walks instead go right or vice versa - try to keep her away from the areas she normally uses to let sun and rain do its best to clean up the areas she previously used.

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