P.S. I have cosplayed Rail Tracer post-massacre before, as well as Two-Face, Zombies, and many other characters that involved blood.
Navigated is right that a straight-up application of stage blood is a bad idea because it is sticky/doesn't dry properly. That being said, Ben Nye or any other professional quality stage blood is still ideal, you just have to know how to use it in a more permanent fashion, which was something I came up with on my own when learning about various "corpsing" techniques (building corpse props, it's something horror designers and halloween prop creators do).
My suggestion for makeup is a mix of 50/50 stage blood & liquid latex. Obviously, you should do a liquid latex test on your skin first to make sure you are not allergic (not many people react badly to it though). Apply that to anywhere it will contact with skin. I suggest liquid latex because it is designed as a form of makeup which is meant to go on your skin. The liquid latex will keep the blood from sticking to everything and from getting onto other people's stuff. You can even coat it in an additional layer of liquid latex once it dries if you're really worried. Liquid latex dries clear so it should be fine.
For my Rail Tracer suit and for my Dune corpse prop, as well as for my Two-Face suit, and many many other cosplay/costume props and outfits I use a mix of 50/50 acrylic medium and stage blood. It is ideal for a more permanent and repeat usage because it will harden and no longer be sticky as well.
To be honest though, I've had my Claire suit for about 3 years and the blood is starting to darken a bit. But I did wear it pretty effectively to about 2-3 cons. And you could probably just reapply more coats of blood if you wanted to rewear with a fresher coat.
Here's a pic of my Rail Tracer (post-massacre Claire).
Also, I do not recommend the suggested method of "filling a tub with blood... and jumping up and down". I do recommend using a bathroom or a bathtub. I believe I laid a bathroom floor with newspaper and then painted the suit and let each side dry before flipping. Bathroom tile or tub is best because it's easiest to clean... However! If you are a purist like me, Claire has a very specific blood spatter pattern which develops as the series goes on. I used all my reference pics from the confrontation between Ladd and Claire atop the Pussyfoot from what I recall.
You can see the scene here:
I took numerous screen caps and then made sketches with pencil and paper to get the gist of where the blood spatters were so that I could replicate a similar blood spatter pattern, then I used paint brushes to apply the blood-acrylic mixture.
Sorry, but I do have to disagree with the "dripping handfuls over the cosplayer" and that "directionality doesn't matter". You could probably just cover it in blood, they're right... and nobody will know any different, but I really am neurotic and it has to be as close to perfect as possible for me.