To answer your question about the bus bar:For inverters they say same size or 1 awg less than the cable powering the device (my manual does). Good rule of thumb to follow.
Can anyone explain what the ramification would be of not grounding the DC negative bus bar? Why should that be done?
You wouldn't want to not "ground" it to the chassis. It improves the (negative) connection between your alternator and starting battery and is another link in the chain where you want good connections. If your charging system is otherwise not connected then it's kind of irrelevant however.
If you're using an inverter and have your inverter case ground wire connected to that bar as you should, then grounding the bus bar actually properly then is actually true ground situation which would allow safety devices such as a GFCI to function properly via the borderline black magic that makes them work.
While I can't tell you if it would or would not trip without it, I do know that it's designed to be at the same or very similar potential as any unfortunately involved person to ensure it detects the fault and stops it before you get hurt or die.
If you don't do that you can wind up with a hot case at 120/240 volts ac, or worse other things in the system become electrified.