put the regulator and moisture trap between your tank and your airbrush, not between your compressor and your tank. The tank makes a storage resevoir to reduce or eliminate the pulsing you can get with a compressor with no tank - sort of the air pressure equivalent of an electrical filter capacitor - storage. The moisture trap is actually more effective after the air has had a chance to cool down (it can get pretty warm at the output of a compressor) and it will do a better job at the output of the tank, too. For car (full size) painting, etc, they recommend running quite a few feet of metal pipe between your compressor and your water trap for that reason - the air cools down, the moisture condenses, and the trap can remove it.
I'm not all that familiar with the D500 - does it automatically cycle on and off like the Badger 180-11 does, or does it run continuously, even if you have an AB hooked to it and no airflow? If it cycles automatically, you should just have to hook the compressor output to the tank with a "tee" type fitting, and hang the filter/regulator on the other port of the tee. If the D500 doesn't cycle, you'll want to figure out how to get a pressure gauge on the tank side of the regulator, so you can cycle the compressor yourself. That auto air bottle I posted the link for is rated to 135 lbs of pressure, so you should be ok with a D500 - but it's still worth keeping an eye on the tank pressure to make sure you're safe.
LOL - I guess I should practice what I preach, eh? When I was a kid (many years ago...) my Dad set me up with a compressor from an old freezer and a freon bottle (30 lb size) for a tank, so I could use my airbrush without having to buy all those cans of propellant. He told me not to go over about 50 psi in the tank. Heck, he even set up the freezer compressor with a spring loaded switch so I had to stop airbrushing and hold the switch on if the tank got low. Being a "bulletproof" teenager, I quickly found that a rubber band would hold the switch on, and that old freezer compressor would put 125 psi in that freon bottle.. not real smart, eh? I'm not sure what old freon bottles are rated for pressure wise, but I think today I'd listen to my dad's advice and stay around 50 or less.. :) Well, maybe 60..