Which nebulizer do you use? There are some with steroid alone, steroid plus long acting drug to open the airways or rescue inhalers. All inhalers may leave an aftertaste especially the steroid inhalers which may cause this problem and may leave drug residues in the mouth. To reduce this problem you must rinse your mouth after each use with warm water and you may also gargle with a mouth wash to alleviate the aftertaste.
Moreover, when using steroid inhalers you must maintain good oral hygiene by flossing and brushing morning and night and change your tooth brush once a month. Steroids weakens the immunity and by doing so they raise your chances of getting oral infections and you can minimize this problem by changing your tooth brush once a month. Also, make sure you use your inhaler properly to ensure the spray mouth piece is aimed at your throat and not your palate otherwise most of drug ends up at the top of your mouth leaving more drug residue in your oral cavity rather than your lungs. Hope these tips are helpful.