Yes washing the area around the rectum is reasonable and one way to do that is to use a sports bottle with warm water so you can just flush that area to remove the stool using the spray end on the sports bottle to direct where the water goes. That way you will not overly stress her or get her all wet and chilled.
You can use a folded towel under her or if she will sit in a sink that you can bleach out later you can clean her there.
With the bloody stool this might be a number of things from intestinal parasites, to inflammatory bowel, to a swallowed non food item injuring her digestive tract (string or ribbon or a plant for example). That could cause vomiting too.
But health issues such as an intestinal infection, kidney or liver problems, pancreatic inflammation all might be a part of this.
Pepcid is a medication that is typically safe to use with an ill cat if you have access to that it might help. You can read about using it here just close any pop up windows so you can scroll down and read cautions and dose info
http://www.petplace.com/drug-library/famotidine-pepcid/page1.aspx
If your cat seems really low on energy you can try a few drops of sugar syrup such as Karo, Pancake syrup or sugar and water on the tongue to see if that helps her.
If there is emergency care available to you here are some things to check to help you decide on using that-
If your cat appears dehydrated (see if a pinch of skin over the shoulder blade stays stuck in a tent form or flows back down normally when released), is not eating or drinking, isn't urinating or passing stool, has a rectal temp over 103.5F (normal is 100.5-102.5 Fahrenheit or 38 - 39.2 Celsius ), has gums or tongue that look white, blue, gray or yellow tinted where they are normally pink, has a slow color refill if you press on a pink area of gum or tongue, is having difficulty breathing, or is becoming more lethargic and non responsive to you as time goes on then you may want to get the cat in to see an emergency vet if one is available in your area.
Otherwise you may want to see your vet first thing when they open.
Hope this helps you!
Cat Health, Behavior, Care Expert
30+ years cat owner, rescue, breeding, study of behavior & health care