Left DC essential failure, from Eddie's notes.
By all means go through the QRH procedure, it could work. But if you end up without the bus, you should suspect a short in a system powered by that bus. Going through the Master Table of Electrical Component Availability, EA-17, it looks like you are in pretty good shape as long as you have the other essential DC bus.
Now for a bit of controversial thought:
What follows comes from the references shown below. Where I think it helpful, I've added my own comments in blue.
DU1 or DU4 are gone, the PFD has moved inboard, and that side's display controller and CCD are inoperative.
If an essential DC bus loses power from its essential TRU, the AUX TRU should take the load automatically. If that doesn't happen, the battery should take the load. The QRH has you check the battery switches on, they should be. Then it has you try the HMG to force the AUX TRU into action, but it should already have been switched automatically.
You either have a combination of faults (automatic TRU switching, automatic battery switching) or you have a short in a system connected to the affected DC essential bus. That being the case, you want to prepare yourself for landing by give the duties to the side of the cockpit still working.
[G450 Airplane Flight Manual, page 03-04-20]
NOTE: To avoid shock-loading the HMG, make each ESS switch selection one at a time. Allow at least ten (10) seconds between each selection to allow HMG loads to stabilize.
NOTE: Only DU 1 and DU 4 are available when using the HMG. To view synoptic / system pages on DU 4, select the PFD-CMD to L (Left), engage the autopilot (if desired) and select MAP on the copilot display controller. This will result in I-NAV being displayed on DU 4. The copilot Cursor Control Device (CCD) can now be used to control display of 2/3 synoptic pages and 1/6 system pages. The copilot display controller can be used to control display of 1/6 system pages.
NOTE: If the sequence of events leading up to the condition of having the two DUs available involved an electrical break-power transfer, it will be necessary to first unlatch the display format configuration conversion by holding the display controller "2/3" selection switch capsule in the depressed position for three (3) seconds before selecting the MAP switch capsule.
NOTE: If the L or R ESS DC bus is not recovered, the display and navigation capabilities of the respective side of the cockpit will be degraded. If the L ESS DC bus is not recovered, DU #1 will be lost and the PFD will transfer to DU #2; additionally, the Left Display Controller (DC) and CCD will be lost. The lost DC will result in the PFD on DU #2 displaying only default settings that will not be able to be adjusted, other than the altimeter setting that may be changed with the DC BARO knob. If the R ESS DC bus is not recovered, DU #4 will be lost and the PFD will transfer to DU #3 with the same default display limitations. It is recommended that the crewmember on the side with the operating DC and CCD fly the airplane for approach and landing.
At main gear contact with runway, ground spoilers should deploy automatically. Manual speed brake deployment is a recommended backup procedure.
NOTE: Thrust reversers will be available only if the corresponding Essential DC bus is powered and hydraulic pressure from the corresponding hydraulic system is available, i.e., left thrust reverser operation requires Left Essential DC bus and Left Hydraulic System; right thrust reverser operation requires Right Essential DC bus and Right Hydraulic System.
FSI G450 PTM, FlightSafety International Gulfstream G450 Pilot Training Manual, Volume 2, Aircraft Systems, October 2008
FSI G450 MTM, FlightSafety International Gulfstream G450 Maintenance Training Manual, August 2008
Gulfstream G450 Aircraft Operating Manual, Revision 35, April 30, 2013.
Gulfstream G450 Airplane Flight Manual, Revision 36, December 5, 2013
Gulfstream G450 Maintenance Manual, Revision 18, Dec 12, 2013