I have one of those alum bars. It tightens the skin with a very noticeable sting and might be good for very tiny and very superficial cuts, but it doesnt really stop the bleeding as such.

There's a very effective way to stop bleeding, that doesnt sting at all, and is very cheap, too: hydrogen peroxide. I have a small bottle in the bathroom just in case. I use it mostly when a family member cut themselves, say with a kitchen knife. Pour the stuff slowly onto the open wound for a few seconds, stop and watch: it foams lightly, white in color, dries within seconds and that's it: no more bleeding.