Belly dance costumes are pricey items so we want to be ultra careful with them. But sometimes you might like to clean them. There are several things you can do depending on the type of costume. I have never owned a costume with mesh parts, so I can not give any advise on those, but I can for the regular bra and belt sets.

Depending on the type of beads on the costume, it’s sometimes possible to wash a costume. I have done that with a Bella and it worked fine. I used a mild shampoo in luke-warm water. I placed the costume in the soapy water for a while till I was sure the thing had a good enough soak. After I did a lot of rinsing, because you want to make sure there is no residue left. I dried all the pieces flat on a rack with lots of fresh air surrounding. Another thing I did with that same costume, but this is not always necessary, was taking of the lining and metal wire in the costume (you don’t want that to start rusting!) After the costume was clean and dry, I replaced the wire with new wire and put new lining on. Not all bra and belt sets have wire, some Turkish costumes have, but not often. One thing that’s very good for keeping costumes nice and fresh is airing them after each performance. Some dancers line their costumes with terry towel fabric so they can take that out and wash it instead of washing the whole costume.

You can probably also get a costume dry cleaned, but make sure to inform the dry cleaners properly about the fabric and beading and ask if it’s possible. Plastic beads might not react well with chemical cleaning.
As for skirts and veils, that totally depends on the fabric. Airing is always recommended. But if you want to wash the items make sure you do it according to the type of fabric. For storing my costumes I use plastic containers. I wrap my bra and belt sets in towels and place some of those special sachets in the containers
that keep it all dry.