It's dirty but it works.

I'm of the opinion that it's important to maintain a good ratio of following:followers

If you follow 10,000 but only have 100 followers then people will assume you're spam and not follow you.

You can also use something like http://quuu.co/ which automates the posting of content via Buffer.

Alternatively, you could just join Twitter conversations naturally and build your following that way.

In my experience, Twitter doesn't give the best traffic (both quantity and quality) compared to other acquisition sources.

For example, for a music app/site you would get strong and qualified traffic from Facebook ads, targetted at users who like the artists and record labels you feature. Or you could look at Pinterest, posting album covers.

One of the best for me has been Medium, way more effective than any blog I ever had. Probably because of the built-in userbase, and the SEO efforts that any blog would have to take a huge effort to build up.

Traffic through Twitter are mostly spam in my experience (i.e. 0 seconds spent on page). Although if you can get a viral topic going, that is generally a little better.

2- Find if they publish any blogs with RSS fields

3- take those feeds and build an IFTTT script to publish links to those blog stories, you can also link to them through your own automated story aggregation site (you can use IFTTT to publish to Tumblr, adding links to your own product concatenated to the RSS story.

4- Be ready to turn your IFTTT bots off at any moment, if necessary

5- Eventually because you've been automatically published links to stories with the same context, other Twitter followers will find your Twitter feed.

6- Prepare yourself to suspect that the majority of Marketers' Twitter accounts may not be all human after all /s

Follow and engage a few verified users in your niche, maybe they'll follow back.