Hey, Nao! It would sound better to say, "My bag was stolen." "Got stolen" is not really proper English. :)

Subject + get + object + past participle (got my bag stolen) mean you had someone do something. For example, "I got my nails done" means you went to the salon so that staff could make them pretty. So, by saying 'i got my bag stolen', it implies you asked someone to steal it, which wouldn't make much sense, unless it's an insurance scam ;)

Either is understandable and they express the same meaning, but my bag got stolen, or even better, my bag was stolen, is more common.

バッグを盗まれた。This is probably the sentence you had in mind. Because in this special type of passive voice the bag is object (and not subject like in Western languages), "I got my bag stolen" would fit better into the Japanese pattern. Still, this is not exactly what you would say in English... unless you hired someone to steal your bag... if that makes sense.

My bag got stolen.