Do I need a relay for my LED bars?
Change your battery first.

Unlike cars which use alternators, ATVs and motorcycles get power from very simple stator generators. How it works is that there's a permanent magnet on the flywheel which excites a stator coil, which is followed by a bridge rectifier. Unlike an alternator, regulation is done by measuring the output voltage and then shorting the stator coil to ground with SCRs. 

How does the system convert rectified AC pulses to DC? It treats the battery as a capacitor. And unlike a car, the system is 1-phase, so the voltage does drop to 0 twice every revolution. 

When the battery fails, the pulses and noise aren't filtered out, the regulation becomes poor, and you get overvoltages, killing the LEDs.