I am not too proud to ask all of my buyers for 5 star reviews. Get some good reviews under your belt and respond to questions as quickly as you can. Fiverr will start slowly sending orders your way. Post your gigs here, reddit, twitter, blogs.
Do you have a blog? Perhaps you can write informative articles and blog posts as part of a content marketing strategy. Once the posts are indexed, they can help drive traffic to your Fiverr page. You can use Twitter, Facebook, and other social media to promote your posts - and your business.