Are LED bulbs bad for my inverters?
No, LED bulbs are not bad for an inverter. Although LED are Semiconductor devices and work on DC only, the circuitry inside the bulb drives the LED from AC voltage.

The AC voltage coming out of the inverter will eventually be converted to a DC voltage to drive the LED. This will be done internal to the LED bulb unit.

Overall, LED bulbs will benefit inverter by using less current rather than harming it.