When It comes to getting any kind of minor bleeding under control pressure is your number one tool. Find some gloves if you can. If you feel safe and don't have them I would proceed to give care anyway. If I don't feel safe I'm looking around for a plastic bag give me separation from the persons blood and any cut I may have. Once I'm good to go I use as much of my hand as possible to push down on the area hard.
Without peaking I hold for at least 10 minutes. If I no longer see blood coming out from under my hand then I am good to bandage and go to the emergency room. If I feel like a few stitches will get the job done then an urgent care place will do just fine.