A difference exists between dirt and dust. We don't ride dust bikes but rather dirt bikes. A massive accumulation of dust results in dirt but sometimes we ride in the dust on bikes made for the dirt.
Other times we get left in the dust.
Riding in dusty conditions can take its toll on your dirt bike and you. Ever experienced a dust storm? You won't forget it and you get a taste of it when riding in the dust, literally too. When racing Motocross, tracks usually get sprinkled with water to keep the dust down but depending on resources and owner commitment you might be eating dust by the early afternoon or 10 minutes after opening gate drop at the more lowbrow tracks.
Trails though have no regard when it comes to keeping dust at bay. Dusty trails usually mean wide open spaces to explore but with the caveat that you and your dirt bike will get covered in grit.
You can't always predict when you might encounter dusty conditions though desert trails almost always stir up dust and if it hasn't rained in a while you can probably expect to ride in and around dust especially with other riders present.
But dust is mostly just annoying. It coats your dirt bike, it sticks to you, impairs your vision and offers very little nutrition when ingested. Expect to consume some dust when riding in dusty conditions but all things considered it won't kill you and your dirt bike will run fine and likely not suffer adverse effects. But that doesn't mean losing sight of preparation.
Just as you wear protective gear for the ride, you can make life a bit easier and possibly save your dirt bike from issues down the road by implementing some safeguards when heading into dusty conditions.
Bring an Extra Air Filter
Dusty conditions muddy up the air filter pretty quick so bring a spare, already oiled air filter, especially on an overnight trip. You will want to change the filter out for the next day but even on day long quests you might gain some benefit from checking the current filter and replacing if needed.
The new air filter keeps your engine clean, prevents power loss and problems down the road because dirt got into your engine. Don't bother with the air filter covers or panty hose trick like you do in the sand. Dust particles are too small for these filters to work effectively.
Use Maxima SC1 on Plastic
Give your plastic a nice dousing of SC1 or similar. Dust easily sweeps aside and won't accumulate.
Use Quality Chain Lubricant
The chain will attract dust therefore use a high quality chain lubricant. Most lubricants, like Chain Wax, coat well upon first application, then melt as it heats up and tends to stay a little cleaner. Either way, lubricate liberally prior to riding, clean afterwards and then reapply the chain lube.
Toss the Tear-Offs
If necessary, tear-offs work better than roll-offs however you will likely find nothing works best in dusty conditions. First off, you don't want to leave plastic tear-offs on the trails and dust tends to brush away quite easily eliminating any need for a tear-off. Besides, dust can work its way in between the tear-offs making things worse.
Try a Bandana
Some riders might find wearing a bandana somewhat suffocating but you have no other options if the foam inside the helmet mouth piece doesn't reduce the dust enough.
Ride in the Early Morning
Nature does have its own water system called dew. The thin layer of moisture that settles on the ground in the early morning hours helps to keep the dust down. Try riding first thing before evaporation has a chance to remove the ground moisture.
Find Shady Areas
Moisture from morning dew or even prior rains sticks around longer in the shade. A trail with a tree canopy and little sun exposure produces a lot less dust than trails receiving direct sunlight and no covering.
Ride Ahead or Behind
When riding with others, either ride up front or fall back enough to let the dust kicked up from the lead rider settle a bit. In any conditions, you want to see the ground in front of you, therefore, if you don't have visual clearance of the trail because of the dust find a distance that allows for the dust to subside prior to you riding through.
Check Wind Direction
Riding into the wind or even with the wind can leave you in a perpetual dusty state. If the wind kicks up enough to cause dusty conditions try choosing trail routes with a crosswind that sweeps dust away from the trail instead of along the trail.
Whenever you ride a dirt bike, expect to encounter some grit and grime. Wads of dirt generally pose little problem to rider and dirt bike but dust tends to cover you like a blanket and can make it hard to breath and/or lead to an irritating ride. Take some precautions before heading out and if conditions get too dusty wait until you can ride without needing an oxygen tank.