I use 4 60 Liters plastic container to carry all my stuff.
Bags might be better, not sure. I use those containers because that is what Renny Doyle suggested in his book. Bags look better and are probably easier to carry though.
I see you don't have a presure washer and a hose in the gear you carry. Do you ask people to use their hose for washing or do you simply do Waterless/Rinseless washes?
For this job he had a hose/electrical for me to use. Most times I have people drop off their cars at my house. But for this one I thought it was easier to do the car at his house.
If I was going to do this as a rolling business I'd have a van or transit connect with a compressor, water tank, pressure washer, etc.