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Hello, I'm Dr. Deb and will do my best to help you today.
I'm sorry that your cat has brought home this baby bunny but glad that it's alive; however, it sounds as if it's injured in some way, possibly by your cat.
Until you can have him seen tomorrow or taken to animal control or a wildlife rehabilitator (if there's one in your area), I'd gently clean the area that's weeping with over the counter very dilute Betadine or Iodine (to the color of weak tea). I'd avoid hydrogen peroxide since it can retard healing; even warm water will be preferable.
After it drys, over the counter topical antibiotics such as Neosporin, Bacitracyn, etc. can be applied but I'd only use a small amount.
I doubt if you have any Vetericyn Spray on hand but if you do, this could also be used.
I hope this helps and that the bunny's issues aren't too serious. Deb