It depends on the bag and the quantity. You also need to take into consideration how labor intensive is the bag? A sports bag is not as complex to make as a box bag. The Chinese don’t consider 1000-5000 bags a big quantity.
I developed a sports bag that I wanted to market. This was a sling bag prototype, that I was able to get a patent on. I could only afford small quantities.
To get 1000 bags made was going to cost me $10.72 per bag. If I could have afforded to purchase 100,000 bags my price would have been 5.16 per bag. Because I couldn’t get the price down to $4 a bag, I couldn’t compete with the other backpack and sling bag makers. Stores needed to be able to offer the bag at no more then $29.95.
There only one way to find out! Contact a US based manufacturer. Send your sample or your pattern to them. You can send the pattern via a PDF file. Ask for a quote! In most cases you’ll get and answer in 48 hours. If you feel nervous about sending out your designs. It’s part of the game call trust.There not interested in your design, they don’t have orders for it! Second point is this, most US manufactures have a base in China! So they can give the overseas price.
You also need to take into account which Asian country are you talking about. You can get stuff done in Vietnam cheaper then mainland China. The difference maybe quality. The world is in search of the cheapest labor force, even the Chinese. As there labor force grows and expects more, the Chinese invest in cheap labor in Africa.