My low beam and running light on the drivers side of my 2008 Trailblazer is out. I Tried different bulbs and checked the fuse. Any ideas?

I don't know what testing you've done as far as voltage and ground? Note the diagram, see the fuses, check those. The fuses above the relays are hot all the time. The fuses below the relays goes hot when relay is energized. Not only check the fuse, use a test light to check voltage at fuse. There are headlamp trouble codes, these are B type codes, to check codes yourself, at the least you need an obd2 code reader that will work with your vehicle and read manufacturer specific codes as well as p0 codes. The headlamp switch lets the bcm know what is going on with headlamps then the bcm grounds the control side of proper relay.

Just to add, if passenger side works, maybe a bulb problem on driver side? Don't touch new bulb with bare hand, if bulb is the problem?