Here's how we dealt with dusty roads. First, take the long view and plant some trees so they can grow while other things are done. We put in a couple rows of thick and fast growing trees. Over the years, we have learned this does the best job of dust control. We planted one row of American Arborvitae on a four ft center and a backup row and also fast growing evergreen. We used Norway Spruce or White Spruce for that on an 8" or 10' center depending on where we lived.
To help them grow, we watered and fertilized from early spring through mid summer and then again in late fall/early winter. I used dry 19-19-19 sprinkled on the ground the first couple of years and then 21-2-9 in later years. By putting ON the ground, rather than IN the ground, any risk of over-fertilization becomes self limiting based on rainfall. Don't use those darn tree spikes. Plain bagged fertilizer is the cheapest and it's all the same stuff.
We watered one year with a drip hose and that was too much work. What worked was a bunch of 5 gallon buckets with a 3/16" or 1/4" hole in the bottom. Fill with water when it's dry --maybe every week or so and it has a dramatic effect on growth. Bottom line, we would get 3' growth and more out of evergreens where others around us were getting 8". People would give me a funny look when I told them the trees had only been in the ground half the time they thought. The above is the long term and plan "B" solution to dust control if other things fail. Start now.
Oh, buy bare root seedlings (mail order)that are 2-2 or 3-2 (years) old for maybe $2.50 a tree. we planted the first year in 3 or 4 gallon pots and kept close to the house so we could water frequently. Then we planted that fall and cut the pot when planting off so as to not disturb the roots. You don't have to do it this way but we had the pots. We did around 600 trees this way over the years.
To control the dust now, calcium chloride is the cheapest and best answer and you only need it in front of your house. We lived in Maine and that's what I saw used everywhere and it was put down dry with a lime spreader. It was cheap and worked but get input from the neighbors. Calcium chloride sinks into the ground surface, works perfectly and won't damage anything. BUT, get guidance because of where you live plus have the town or someone OK it and maybe even huddle with your neighbors. Probably get them involved and ask them to pay some since one day they will have a common problem and need you. At least get their OK and the town's OK. Environmental laws are written by people that never did it, never dealt with it and often have an ideological prejudice against those doing it. I can only imagine California.