Hi Slimboyfat46
Your 2000 Watt inverter will draw about 200 amps when fully loaded. If you don't fully load it, it will draw less current. It won't quite be pro-rata, as even with no load it still needs a certain current. If you never intend to use its full capabilities then a lower wattage unit will be a bit more efficient (and smaller/cheaper). The e-bike chargers I have seen have been roughly 100 Watts, so unless you are charging a whole fleet of them at once then 2000 Watts seems like overkill.
To answer your original question, the fuse needs to be rated high enough that it doesn't blow during normal operation, and doesn't drop more than a fraction of a volt when 200 amps is passing through it. This means choosing an automotive fuse, I'd suggest something like a 200 or 250 amp mega fuse.
The fuse needs to be at the battery end, so that the wiring is protected. You haven't mentioned wiring, but with that sort of current you will need a large cross section to avoid excessive voltage drop. Minimising the distance between battery and inverter is vital if you want to avoid the need for really thick, heavy and expensive cables.