Dunning-Kruger strikes again - at least use a *galvanised* bucket!
More seriously, if you are not 100% confident that the Neutral of the inverter is isolated from the DC input, and you are powering it from the vehicle battery, if at all possible, drive a ground stake and connect it to the vehicle chassis.
Personally, I'd recommend using a separate deep cycle battery for the inverter, in a plastic portable battery box, so you can either guarantee its fully floating, or ground it as per the inverter manufacturer's recommendations (if any), and also so you don't end up flattening your car battery if you use more power than you expected to.