Marketing is very important in any business. I don't know what your budget is but using Social media (on here, FB, Twitter etc), paid for links / ads on related websites could be used (e.g Namebio). Highlighting it on your own website which it's self has content to draw visitors in, and an email list would be a classic way of gaining eye balls, along with a landing page on the domain it's self, particularly if it has decent back link traffic.
Also I wonder if those with deep pockets actually put out Pay Per Click Adverts as well? Would only be worth it if the target price was large enough. Does anyone actually do this? I'd love to know. Thanks.
In short then, the amount of people who see it will directly increase it's chances of receiving bids. Best of luck with your sale.