What current should be used to calculated the drop across the diode? RMS current or average current?
Ignoring the small glitches as current rises and falls, the diode is only conducting at the top of the waveform so that is the only real place that it will dissipate power.

It's not a perfect value but I'd consider using the value of 3.7 amps at whatever volt drop is seen across the diode to calculate power lost in the bridge diodes. And, of course this power is only wasted 50% of the time for a duty cycle of 50%.

So if 1 volt is dropped across the diode(s), the power dissipation is 50% of 3.7 watts = 1.85 watts. Alternatively use LTSpice to calculate this for you - i.e. produce a power waveform that is V*I and average it.