Yes i take Layla everywhere with me in her purse. Since she was a puppy we would let her investigate it and would do practice runs in the house or around the block. When i take it out she practically jumps in it now. She still always gets a treat when she goes in and when she comes out. And for the most part she sleeps the whole time in there- but its something you have to do gradually and keep up with it and before you know it she will love going in it.
Oh i forgot to mention- i usually drape a jacket or a sweater over the purse- like you would if you were carrying a bag and didn't want to carry your jacket- this usually covers the mesh area enough for no one to see in but that lay can still breath
Also in our family- there are times that Layla needs to be in her purse- we travel a lot and we don't leave her in the car and won't leave her in a hotel- so she comes- and she is good as gold.