How could one go about promoting dropship items offline?

If you're trying to promote the clothes offline, how about going to retailers with samples and get purchase orders? Then, you can bulk order from the manufacturer and have them dropshipped.

As mentioned in the previous posts, you have many options at your disposal, one already mentioning ordering samples to present to local retailers. Other options could involve a more personal approach; use the samples, and talk about them to friends, or better yet, give some of them to friends and family and ask them to mention where the clothing can be optained, maybe blog about them or mention them in their social media communities. Create fliers with QR code to your webshop, and hang them in places where people would gather, or make small cards with the code and ask local stores or bars for permission to leave some on their counter. Ultimately you can add advertising to all of this, both online as well as offline. I hope these few suggestions can give you some ideas to succeed further, best of luck

I wouldn't expect to be able to work a deal out with a local retailer seeing as if they are interested in the product, they would just order from the dropshipping source and take out the middleman (you). I just can't see offline dropshipping alone being a viable option; you're probably going to have to just open a store online and maybe do some offline promotion for your store.

I've been selling clothing online for over a decade, started off on eBay. I've been a consultant for years, in the apparel industry, and have helped several retailers and manufacturers get up and running.

1- Any retailer that will give you a purchase order [for drop ship merchandise] is not well educated (as a retailer) and is bad at sourcing and will be out of business soon. The reason is they have a store and don't know where to get merchandise. if they can't look at your merchandise and realize they can get the same deal, they shouldn't be in business.
2- Doing direct mail is great, but EDDM is too broad for something so niche. You said men's clothing from Asian sites which also means (whether you know this or not), it's sized for that body type. So your typical american male build cannot fit that clothing, even if it is their style. Unless you are talking about the counterfeit merchandise (i.e. fake Gap, Abercrombie, etc., they sell in which case forget it, because that's illegal, google it if you don't believe me).

Having said that, a good tips is this:

Go to a local shopping mall or retail store and offer to bring your own merchandise for a flash sale and promote it. It's a good time, since we're in the 4th quarter and holiday shopping is gearing up. Downside is that you need merchandise, you can't drop ship this way.

I've done drop ship before but I'd never do it with clothing. Too many size/fit issues to deal with and returns. When I did drop ship, I only dealt with low return merchandise.

Tangible products are both the hardest and easiest things to sell online. Easiest because it's easier to get someone to buy a tangible product than a digital/info product. It just is. Harder because it requires more to sustain that business model because of the physical aspect of the merchandise.