3/16" thick may be tough. I've had success cutting up to 1/8" thick with a 2000 Watt Mits.
You'll need to coat the top surface of the bronze with a graphite spray paint. I used Aerodag-G, which works quite well for bronze, copper and brass. It leaves a slight discoloration to the material after removing it with paint thinner or alcohol, but can be polished out. If you don't coat the surface well enough, the beam will reflect off and can be a danger to the operator.
I cut it with continuous wave at 2000 Watts and N2 assist. Light dross was normal but easy to remove. I don't remember the exact settings for piercing, but I do recall that it was a long pierce. If possible, rough up the pierce points with a Scotch-brite pad. Use a fairly slow feedrate. I was somewhere around 30 IPM for the 1/8".
Good luck!