Getting interviewed for a website is a great way to promote your graphic design business. Online interviews will expose your business to a larger audience and drive traffic to your website.
While it would be great if websites came to you for interviews, this will not always be the case. At any point in your design career, you have to self-promote. This can be as simple as contacting a website and asking if they are interested in an interview or case study on your company.
Of course, you should target the right websites with your inquiries. A good place to start is websites that focus on design in general, or ones that focus on a particular field such as package design. See if the website has featured other designers in the past, the type of questions asked, and use that to tailor an email specifically for that site. Let them know what type of work you do and why you would be a good fit for their website.
Another good place to check for interviews is the websites of software you use. Many software companies write case studies on companies that use their products, often with images of their work and links back to their portfolios. 37signals writes case studies of companies using Basecamp, Highrise and their other products, as do companies such as Marketcircle who created Billings. Look at all the products you use on a regular basis and see if they conduct interviews, and contact them with background information and how you use their product. These case studies help promote their products as well as your business.