First let me answer your initial question. No, don't give your cats cipro. It's not very effective, and you can read more below, from the feline vets' association:
It's not a good idea to give an antibiotic anyway, when nothing's been diagnosed. I don't agree with your vet's approach - giving antibiotics to your other cat without a urine sample or physical exam findings.
I'm assuming that all the cats in the house are neutered. If any are not, that could be contributing to the problem.
I agree that's it impractical to bring each cat to the vet (unless any seemed ill, of course). I also think this is more likely behavioral in origin. I realize your household has been stable with your eight cats and 1 litter box in the past. Nevertheless, it is a classic arrangement for inappropriate urination. Even if the cat being picked on isn't doing it, other cats may be stressed by the chasing, hissing, etc. They need more litter boxes.
I normally tell cat owners that they have to rule out physical causes for inappropriate urination first. In this situation, I think the opposite. I recommend addressing the behavioral aspects first, especially since you don't know who's doing it.
As an aside - you should know the majority of feline cystitis in cats, especially younger cats, is sterile - there's no bacteria involved. This illness is not well understood, and because vets want to play it safe, and owners want to do something, we give antibiotics.
The ideal recommendation for litter boxes is one box per cat, AND one for every floor of the house. Now, I'm realistic enough to know that's often not possible. But I do recommend something in between the ideal and what you have now. I would start by adding at least three boxes, one where the current box is, and two others in different places. I would also either keep the cats out of the bedroom for now, or place a litter box in that room, and put some uncomfortable material, like aluminum foil, or double sided tape, on the area being urinated on.
"Cat Attract" is a litter additive that works for some people. Below is more information:
I've known cat owners who swear by it.
Use an enzymatic cleaner on any urine stains. There are several good ones. I like Nature's Miracle:
Even if the cats get along well, there is a certain amount of stress just because of the number of them. A safe non medical way to address stress in the cats is Feliway. This synthetic analog of positive feline pheromones has been demonstrated to improve stress related behaviors. You can read more below:
It's available at Pet smart and online. I recommend the diffusers. Place them in the areas the cats spend the most time.
Other ways to reduce stress is to have plenty of different places to eat and drink, and plenty of resting spots, beds,etc.
I would also recommend separating the cat you suspect now. You could try to get a urine sample at home, by placing saran wrap on top of the box, or using non absorbent plastic granules in a clean box. Bring the fresh sample to your vet for analysis.
Or if the urinating on the bed stops, that will be very telling, obviously. If the urine is abnormal, she can be examined and treated.
If the urine is normal, that cat can be treated with one of the behavioral medications we use for cats. They include Prozac, amitriptyline, and Paxil.
I hope this was helpful. Please feel free to ask any follow up questions you have. I would be happy to talk further with you.