Is there any way to place an object within a store which will change the three shopping bags that spawn on shoppers in that store only? I want to make a clothing store with its own style of bag, and I'm wondering if this is even possible.

As far as I know, the bag spawned when the sims purchase an object is determined by the object itself. If the object contains a custom bag, it will be used; if not, the standard bags will appear. Chenging the bags for one single shop is impossible, to my knowledge (otherwise, be sure that EAxis would have created a custom "H&M" bag for the commercial lots released with that stuff pack )

Too bad, that would have been awesome, have your own stores logo on the bags.

Numenor - do you mean that the bag spawned is determined by the object sitting on the shelf that the sim decides to purchase, or the larger fixture object (like a clothing rack or shelf)? If the latter, why couldn't you edit the clothing rack or shelf unit so that a different bag spawns?

Each "rack" object can contain a reference to a custom "bag"; I put the quotation marks, because you are not bound to use an actual bag: if you have seen the postcard racks that MaryLou and I have created, they use a special "postcard-shaped" accessory, that appear in the sim's hand (instead of the bag) when he purchases a card from the rack. But if the sim buys a single postcard placed on a shelf, there is no custom bag.

The Maxis clothing rack, on the other hand, has no custom bag, and therefore the standard paper bag appears. It should be possible to modify one of the maxis clothing racks, or create a cloned rack, that uses its own bag, but I'm not sure how stable it would be: if you have noticed, when the sims wander in the shop, the bag appears and disappears continuously (it's visible only when they are walking); I think that even if a custom bag is created, it may be replaced by the standard one after some time.