After washing the bag, yes, you could put it through a dryer; most sleeping bags are designed to withstand industrial dryers. Dry in a front load industrial dryer at the Laundromat, since a lot of home dryers are too small for your sleeping bag.
Make sure to dry the bag on the lowest heat setting available, while checking often to make sure the drum of the dryer is not getting too hot. If it gets too hot, the shell or even the synthetic fill of your sleeping bag could potentially melt. Never let the dryer stop unattended, especially if the dryer doesn’t have a cool-down cycle. You don’t want the sleeping bag to be resting on a hot dryer drum, which may cause melting of the outer nylon and zipper.
During the drying cycle you could throw in a couple (max three to four) of tennis balls or even a pair of clean and lightweight sneakers into the industrial dryer, along with your sleeping bag, to gently break up clumped insulation, to restore the loft of the bag.
Take note to check if your sleeping bag is thoroughly clean and dry before storing and/or using. You can leave it out all night on a smooth surface to make sure that it is completely dry, before putting it back inside the storage bag.