First, check all your connections. Grounds and power to the bus. A problem in either can cause this problem.
Assuming you've got a non-exotic (i.e. lead acid) battery:
Go to Napa, pick up a $50 load tester. This is just a big resistor with a volt meter built in. Load testing is the only definitive way to check a battery's health - the battery is shorted through the resistor, which dissipates that energy as heat. The volt meter will show the voltage during this discharge and indicate if the battery voltage is dropping faster than it should.
If the battery checks out, suspect the Alternator. Check the belt tension, probably not the cause, but its easy to fix. You can check the alternator output with any multimeter, it should read ~14v regardless of throttle. A multimeter with the ability to measure current will tell you what the amp output of the Alternator is.
If all that checks out, I've got no idea where to go next.
If you're all about the destination, take a fucking flight. - Frank Turner
Got brap, and twice as much fuel as you. - Akarob