You need to figure out what you're protecting with the fuse. That's what determines its size. Generally this will be the wiring after the fuse (so that it doesn't start a fire).
For the bus bar connections, you can size the fuse based on the safe current carrying capacity of the bus bars and their feeder lines. If this is greatly more than could ever be expected to flow through them, it may make sense to use a smaller fuse than this maximum. Wiring that connects to the bus bars, if of lower capacity than the main fuse, should have its own fuse or circuit breaker to keep it from being overloaded and starting a fire. Usually this is the case when you have a bus bar—the main fuse for the bus bar is larger than most or all of the connected system's safe current carrying capacity.
For 2 gauge wire, it appears the NEC permits 95A (for 60°C insulation), 115 (75°C), and 130A (90°C insulation). The inverter probably would be better served with heavier wiring than 2 gauge. You presumably need to size the system for the maximum inverter draw plus the maximum simultaneous draw from other 12V systems used concurrently (lights, fans, etc.); solar if active will offset this current some, reducing the current coming from the battery. If you will have a large solar setup, the charge current from it may be the highest current you need to size things for.