How to keep paint from getting dusty while drying?

Not too much, basements are dusty, dust is everywhere, housekeeping will help mitigate it some,but dust is everywhere, you just have to keep up with it, protection of painted model is the key.

Ask your mother about keeping up with dust in the house,my wife says it's an endless battle.Everytime I get in the car I dust the dash board.

Speaking of dusting the dash, 

I've started using a car dash dusting mit to wipe down the model just prior to painting.

I was wiping them down with a cloth or paper towel. The problem is that that was imparting a slight charge on the piece making it a dust magnet. The mit helps pull the dust off without giving the part a slight charge. I suspect it actually removes what slight charge it present. All I know is the kits are MUCH less dusty. 

Some parts I let dry in my paint booth, some on my work bench. 

Hope this helps.

EDIT:

What type of paints are you using? I use mainly enamel and Tamiya paints. I brush paint,

rattle can paint, and airbrush paint. The Tamiya dries VERY fast and that helps with dust.

The enamel dries much slower.

I have a homebuilt drying  box.  It has a 60W light bulb with a dimmer to supply heat when I dry enamels.  For fast drying paints like lacquers I just pop it in the box but do not turn on the heat.

For reducing dust in the shop I am looking at building a dust collector like carpenters use in there shops.  Check out the ads in a woodworker magazine.  I had made a homemade dust collector for the shop year ago and it didn't work that well, but I hope to create one of those new vortex cleaners like in the ads.

I have a homebuilt spraybooth made from an old kitchen cabinet. It has an exhaust fan that is connected by a heater vent to a board that I put in the window when in use. The cabinet has a piece of material in the front that I close after painting and leave the fan on. It pulls air thru the material which traps the dust but lets the air flow thru drying the paint. The material is what is used for sheer curtains. If you don't know what they are, ask your mother. Every once in a while my wife will take it off the cabinet and throw it in with the wash. It collects all the dust. I've even sanded wood right next to the booth while a model is drying and got none on the model but could see it on the curtain.

Jim 

Stay Safe.

Tojo72

Ask your mother about keeping up with dust in the house,my wife says it's an endless battle.Everytime I get in the car I dust the dash board.

 

Say WHAT? "Ask your mother about keeping up with dust in the house?" Seriously? You're concerned about dust, then dust. 

I had an extra 25 gallon clear storage tub that I had use.  The model goes on the lid, and the tub goes over it, upside down of course.  Works like a charm, and our old farm house is very dusty and cat hairy.

I lay down a clean microfiber towel, put my model/drying jig (whatever that happens to be) on top of that, and then cover it up with an upside-down, large Gladware container.  The microfiber towel lets things "breathe" while completely sealing out dust.  Granted, it doesn't work for anything much bigger than a car body, but the flat, thin finishes on my military aircraft models don't stay wet long enough for dust to be an issue.

To make sure dust is removed before painting, I just give the stuff I'm painting a quick blast from a can of compressed air.

Aside from that, I have air filters that run 24/7 in my apartment, and I dust the whole thing top to bottom every couple of weeks.  Keeping everything clean to begin with eliminates a lot of issues.

If you have the room you can get a fridge that doesnt work for dirt cheap I drilled a hole in mine and added an extra bulb but it keeps the dust away quite nicely

I build small models, so I just put them to dry under the tall cover of a Costco cake tray

Here is what I use:

And it keeps the models completly dust free, these have been in this tub for about 7 years :