It is very possible to bleed your own brakes. You just have to be familiar with the system and be able to multitask very well.

You can use a tube that goes over the valve and right into a bottle. Fill the reservoir up and start pumping. Pump a few times, and then check on the reservior. Then check on the valve. If you use a clear tube, you can see whether or not it is new or old fluid coming out.