deep bedding for chicken run vs plain dirt?

What do you use for deep bedding ? Is plain dirt better as chickens do take dirt baths to clean themselves. Dirt baths are proven method to get rid of parasites in animal world. Horses and other big animals do dirt baths too. I noticed my chickens often do dirt bath especially under direct morning sunlight. It created lot of dust around chicken run area. I read some online articles about using pine shreds as deep bedding but that would prevent chickens from taking dirt baths, right? I don't know if pine shreds prevent dust from flying all over the place either. my outdoor chairs/table are as dirty as ever. Thin cover of dust in couple weeks after washing.

Anyway, my chicken run is a mess b/c young chickens are shedding their young feathers. I was thinking of buying some materials to make deep bedding for the chicken run but not sure if that is a good idea given the benefits of dirt baths or it helps with cleaning up the feathers.

Please sure your experiences with whatever works best for you so I can get some idea for next step.

I use deep litter pine shavings in my coop area and grass clippings in my run. The run really isn't the deep litter method because I don't turn it over for composting. It degrades by itself and I add to it each month when it thins out. They can easily scratch all the grass out of the way to get down to the dirt for dust bathing.

Post your climate/location to give people a better idea what advice to give.

I am in northern California. hot/warm during summer months. cold during winter but no snow. It rains during winter months. Half of the chicken run will be cover during raining season. Chicken run is about 8x24 ft.

it's been raining last 3 days and the chicken run is totally muddy. Worst, chickens are drinking the dirty water from the mud puddles. yikes!

the chicken run is 8x24ft. I wish I cover the whole thing instead of half like I have right now.

I live in Ohio and we get plenty of rain here. I plan on using pea gravel for the run, about 4-6 inches deep. I am using pea gravel because the farm where I buy my chickens uses it and the owner swears by it. She says it drains well and can be hosed down. I just need to keep the mud under control. If you are concerned that your chickens need a dirt bath area just leave an area of dirt in the run walled off from the gravel with some 2x8 or 2x10 boards