The air inside department stores is MUCH worse than the air outside. Yes, it may 'feel' cleaner but department store air where there are clothes on display is filled with dust of various types from synthetic fibres which is even more toxic than normal outdoor dust and much more allergenic to many people. Plus, the powerful industrial air con systems they use in those stores circulates around any viruses that may be in the air from sick people. You'd be better off taking your chances on the streets than inside shopping malls.
Simply buy yourself a bicycle. Easiest and quickest way by far to get around central Bangkok. It's almost completely flat, so dead easy to cycle around and you'll be amazed how quickly you can get anywhere. Plus, of course it's free and counts towards your daily exercise. Just buy a sturdy bike lock (preferably two) and make sure you lock it up well to a lamppost and remember where you put it. You can also attach a child seat on the back for the Thai GF. Works fine as long as she's not over 50 kg. Another basket for carrying shopping on the front. Perfect solution.