Are you looking to dropship just lingerie or other products as well?
Dallas here from the Social Care Team at Shopify.
There are actually a lot of different suppliers for drop shipping in the United States of America.
Apps like Oberlo and Aliexpress are a great place to start. Although most of the suppliers are Chinese some products have American suppliers as well. If you would prefer your products to come from the USA you can choose that option. I will add, though, that when a product is shipped from China and a product is shipped from the USA, they are actually the same product. One isn't 'better' or 'worse' than the other. If that was the reason you were looking for only American suppliers.
When it comes to dropshipping and choosing a proper supplier it will depend on what you are wanting to sell.
If you want to sell clothing like lingerie brands like this will be able to help you get started.:
For general products, companies will be good to look into just because they have the option for lingerie as well:
Also, have you looked at our Shopify Academy. It is free. It won't necessarily help you choose a supplier, but it is really useful when it comes to getting information on how to run the best drop shipping business that you can have. There is a series called Dropshipping 101 by Corey Ferreira that has some amazing information that should help you get your website to make some solid sales. Another thing to look into is this really helpful blog post from Shopify Blog called the Ultimate Guide to Dropshipping. It will give you more ideas in greater detail when it comes to getting your dropshipping business up and running.
If you have any more questions please let me know and I will see what I can do to help you further.