In 30 years of off-road the problem has diminished quite a bit, but still horrible and does happen.
I use exactly that method:
1 twigs
2 drag across grass sideways
3 (optional) find a dusty patch and ride across it
4 large bin bag kept in car boot which you put right over contaminated wheel and pull tight
I think the suggestion of water is very problematic - that normally just spreads this nasty stuff and risks contaminated water droplets being inhaled or ingested - nasty for health.
So....4....is what I would add. We keep v large and tough 100 Litre plastic bags with draw ties in the wagon. If we get infected we do 1-3 always, then bag up for drive home. Clean completely back at base.