While vacuuming, I heard the typical 'kaclink kaclink' of a larger solid object being sucked up. I think it might be an earring I lost a few days ago, so I'd like to get whatever it is out of the bag. How can I do this while minimizing the amount of dust gets back into the air?
Try using water.
Take the dust and put it in a plastic garbage bag and then add water slowly while holding the bag as shut as you can.
Now that the dust is wet you can handle it without it blowing in your face. Add the mixture slowly to a bowl or buckets of water and the dust should float making anything appear.
If the earring is big you can sift through the wet dust. Please do either method outside so that any spilt dust does not go in your face.
Get a second vacuum with a hose attachment. Over the opening of the hose, attach (with duct tape?) a screen that will let through dust and dirt but nothing bigger than, say, a popcorn kernel. Then simply vacuum all the dust from the first vacuum's bag into the second vacuum's bag through the hose. The larger object -- such as an earring -- will get caught by the screen or will just remain in the first bag.
The trick to this for me has always been surface area. I cut open an old grocery store plastic bag, and lay it on a table. I then cut open the dust bag, and carefully spread it into as thin of a layer as possible so that there's no need to dig a lot. Cleanup is simple: fold the grocery bag to seal the dust.
In general, you're trying to avoid getting dust into the air column, and the surest way to do that is to disrupt the pile as little as possible. If the depth of the pile is thin enough, you should be able to do a quick visible inspection in order to find your lost trinket.
I also tend to use a pair of tweezers to work through the debris or fish things out of the bag when I can see them towards the top.
If the biggest problem is making a mess, I would take it outside. Having some dust fly around there doesn't really seem like a problem. And if some of it does reach the ground, rain (Or a bucket of water) will wash it away soon enough.
The dustbag contains not only dust and dirt - it's also heaving with bacteria, so although I do exactly what you now intend to do, I first take the precaution of wearing a face mask (just a basic dust mask) and rubber gloves. If you can, take the bag outside and spread a sheet of something (plastic, tarpaulin, whatever) and put the bag on it. If its disposable, then slit it open and rummage for what you want, if not, you'll have to either put your hand in and rummage, or gently tip and pull out the contents onto your sheet and poke around to find the object. Best not done on a windy day... and after all that, I hope it is your earring and not something you don't even want, like a bottle top!
If you can find someone who has a metal detector . . . with two large plastic trash bags, sort half of the debris into one bag and test it with the metal detector, keep dividing the contents by the results of waving the metal detector over the bag.
Get a really strong rare earth magnet and run it around the part of the bag that would be the top of the dirt pile. If you feel it connect to something, bring it to the top of the bag and then try to pull it out with your finger. If your earring was a non-magnetic metal (which is most likely) and this plan doesn't work, it's likely you will feel extreme rage having failed after all the trouble of getting the magnet. To handle that, tell the vacuum you hate it, optionally kick it a few times, then tell it it's sacked. Then go watch QVC so you can buy a new earring.
One method to recover the potential earring would be to take the bag to an open area where making a mess would not be a concern, and just splitting the bag and spilling its contents.
The wind will carry away the dust and fine particles (hold the bag from upwind) and the earring and other heavy objects will fall straight down. Just be sure to clean up the bag pieces and other large refuse so as to leave the area unpolluted.