I would not advise you to do it with a knife! You have to know your biology/anatomy pretty well. Also depending on your fat% finding the artery that runs through your wrist will be a pain in the ass. Plus, you have to cut the artery lengthwise and then hold it into water so that no clotting can take place. And to top this off, now you need to do the same thing to your other wrist with one fucked up hand. You will probably cut tendons involuntarily and then lose dexterity.
So you say you have no bath, that is a big problem - I would not do it then.
If you really want to bleed out then I would advise one of the following:
1) Get a bath (a big plastic container with at least ~150 litres) -> Drink alcohol + take aspirin -> Cut your femoral arteries (within upper thighs) -> Bleed out it 30 - 60 seconds -> Death
2) Get a blood draining kit (online purchasable), preferably those butterfly needle kits -> Drink alcohol + take aspirin -> Go to an isolated place -> Drain your blood until loss of conscience -> Death
I would not advise you to do it, there are better methods. But if you are really determined I would say go for the blood draining kit!
Here are some pics what arteries you want to cut (in the pictures it is both right arm and right leg)