Yes. Women can wear shorts in Bangkok. They can wear anything they want to wear. Is it a good idea though? No. It is disrespectful to the buhddist religion. Women don't show much of anything and it would be like someone coming to your nation and wearing something that is totally unfit for what you stand for, maybe wearing nothing at all.
Sure, you can ultimately wear anything you please and many do. But if you are going to a place to see their culture and experience what they are about, it would be far better to have the respect for them that you would hope they would have for you if the tables were turned.
Long shorts are more appropriate if you are going to wear them or a coulotte set that is similar to a dress. You might give the wrong impression if you go wearing short shorts outside the house. And you certainly don't want to do that.