I'm looking for an icon that will clearly identify the "shopping cart" for an apparel store. A shopping bag? A Cart? Is there any other specific icon?
If we go further, do you think it is better to display an icon? only text (bag / cart?) or both?
Oh, there are a million! Of course, depends on use, size etc, but here are some suggestions. These are taken from icomoon and they have a lot more. What makes sense, is either a shopping trolley or a shopping bag a lá google store:
The shopping cart is essential to a shop and it is easy to display this function as an icon. So I would definitely use an icon and if you have enouph space available, put the label on it as well. Use a cart if you would buy your products in a cart in real life (hardware, food, etc.), and use a bag, if you would buy your products in bags in real life (clothes, jewlery, etc.)... ;)
As you and others have mentioned, a shopping trolley/cart, a basket and a bag are all well known icons for this purpose. As user568458 pointed out, a bag is probably best for clothing as a trolley or cart could make people 'think of supermarkets and high volume, low quality discount shopping'
With that in mind though, how about a gift box icon as an alternative to a bag?
As user568458 pointed out in the comments an open box may be preferable to avoid confusion.
In some clothing stores, they wrap your purchases in paper and place them in a box, if this is something that the store that you have in mind might do then you could mimic this for the online shopper by using a gift box icon, perhaps with the logo of the store on it.
As for displaying icon/text/both I would suggest icon only but if you hover over it then a little text box comes up. This of course is dependent on your design though and how quickly you think your users will understand your icon.