I have a wall switch to control a bedroom ceiling fixture at the end of its run (2-wire power source). I would like to install an additional switch/closet light connected to the end of the run. I understand that I need 3-way switches and 3-wire cable and that the ceiling fixture needs to be energized for the closet light to function but I am unsure of the wiring configuration for such a setup.
If the wall switch only has 2 wires, it is called a switch loop. The closet light and switch cannot be extended from the current switch. The closet switch and light need a neutral, and that seems to end at the lighting fixture.
If you can run a two wire cable from the fixture to the closet switch and then to the closet fixture, the setup is simple:
Connect the neutral in the new cable to the neutral in the old fixture box. Connect the hot in the new cable to the hot in the fixture box. This is also connected to the hot going to the old switch loop.
In the new switch box, connect the neutral to the neutral in a new cable going to the new closet fixture. Connect the hot to one side of the switch. Connect the hot going to the new closet fixture to the other side of the switch.
Based on what you've provided, I made this diagram to go along with what all you will need for the new installation and how to accomplish it. This is the only working solution without first running a new neutral from the existing light down to the existing switch. You will have to pull power from the light, not from the switch. Also, as you had mentioned, this switch will only work when the bedroom light is on. However, you will not need a 3-way switch (that wouldn't help anything) and you won't need 3-wire cabling.
The red blobs are wire nuts. Black is hot, gray is neutral, and green is the ground.
As you can see, you'll need two runs of 2 wire cable. The size of the wire should match whatever amperage the current breaker is rated at for this circuit; 12/2 for a 20A breaker, 14/2 for a 15A breaker. Then you'll also need your new lighting fixture and a single pole switch.
One last mention, as it might not be the easiest solution, but would probably work the best, is to run a new 3 wire cable from the existing light down to the switch, and pigtail the neutral so that you now have the neutral in the switch box. Once this is done, you'll be able to add your new switch and light tied in to the existing switch. In this case, it'll also work independently of the bedroom light.