It depends on your charger.
Bosch actually makes three chargers for their batteries, the standard 4A unit, a smaller 2A unit, and a 2A unit with a 12V input that does not appear to be sold in the US. Given the cost of Bosch stuff, you'd be much better off with a cheap inverter and a standard charger. The amp rating refers to the 36V output not the 120V input.
4A x 36V = 144W, in theory a 250W inverter would work as long as it didn't fry your car's electrical system assuming the charger wasn't terribly inefficient. You'd need to be on a car circuit with a 20A fuse to be safe.
I plugged my Bosch 4A charger into a generic 250W inverter plugged into my truck and it charged, but the inverter got pretty hot, so it was definitely working hard.
YMMV.
BTW, don't try to charge your dead ebike battery off your car battery without the car running. Your car battery will probably be dragged down to where the car won't start.
You can get powerpacks like the expensive "Goal Zero" ones with built in inverters and enough amp hours to charge your ebike battery. I found a closeout Schumacher Storm 700 that will give me about two 60% charges on my Bosch 500wH battery. I needed something like that for my camper so I bought it for that purpose, but it does work great for the ebike as well.