If you use a machine, use only a front loader. A top loader is likely to destroy the bag.
You don't say what type of bag--down or synthetic...
I recently washed a down bag by the following method (should also work for synthetic):
1. Hand wash with down soap. When you pick the wet bag up (it can weigh 30-50lbs) cradle it from below. If you pick it up improperly, the weight of the wet down can rip out the internal baffles.
2. Place in top loading washer and use ONLY the rinse and spin-dry cycles. (I carefully placed the bag around the tub so the agitator never worked on the bag and the baffles were never stressed.) If you don't have access to a washer or spin-dryer, squeeze water out carefully.
3. Repeat 2 several times until all of the soap is out.
4. Dry by hanging on parallel lines to support it horizontally (like a hammock, or better yet, use a net hammock) and blowing air on it with a fan. Takes several days. Every few hours, use your fingers to break up the down clumps (down only).
Another method of drying is to place in a dryer at the LOWEST heat with some clean tennis balls (down only, to break up the down clumps.) Do not overheat--may be worth finishing by 4 above.
Dry cleaning must be done using the proper fluid. The most common cleaning fluids will destroy the loft of the down. (And many cleaners who claim to know how to clean down use the wrong fluids...) Air out the bag to remove fumes. Many (most?) experts disrecommend dry cleaning.
BTW, the smell of cat urine is very hard to remove. I have read of cleaning enzymes that can be used to do this. (Don't know any brands off hand, may be available at a pet supplies store.) I have no idea if these cleaners will damage the down. (Down is rather delicate--if you remove the oils in the down, you will reduce the loft. Wet down can also be damaged by rough handling.)
Doug