At 12 volts, 110 watts comes out to about 9.2 amps. The gotch is that incandescent lights pull more current when they are cold, so you get a current surge when they are first turned on.
So, the running current is really close to the fuse rating, but the switchon current is a bit more. At exactly the rated current, a fuse is not supposed to blow, then there is a specific curve of overcurrent vs time to blow. I don't know what the spec is on the mini fuses.
Bottom line is that it would be a good idea to switch the light bar on only when the engine is idling, otherwise, you will probably have no problems. Traditional Brit and Yank engineering practice is to add in a 30 to 50% safety factor in component design so the relay and wiring should be OK.
