How can I bring more business to my company that provides VA services and data services?

In short your answer is Content Marketing.
You are correct, freelancing sites aren't meant for companies they are for individuals looking to supplement even if you do have your random freelancers who do make a decent living out sites like that.

My name is Humberto Valle, I'm a globally recognized competitive strategist and founder of www.Unthink.me - An inbound marketing agency, known as the most helpful agency in the world. Unthink's primary expertise is service based businesses which sell intangible products and value, such as yourself.
If you are depending on paid advertisement and freelance type of sites I would assume that you have a simple website with a very minimal or nonexistent blog and no content strategy. Possibly even a weak website SEO. I recommend that you read my article provided below; it will give you great insight on what exactly is Inbound Marketing and how it helps generate sales! Pretty much any business can benefit from inbound marketing but it has to be done right. You can't just write content for the sake of writing. Follow these general steps:
1. define your ideal targeted customer and their interests and daily routines (in/out of work)
2. define their 3 stages of their Buyer Journey and couple each of these stages with how/when each applies to their personality, hobbies, interests, routines..etc.
3. Write a list of possible topics that your persona will be interested in, no bad or good answer.
4. narrow down your list by coupling the best topics with the possible best stage in their cycle and one that matches their daily routine or interest during that stage.
5. Repeat this for each of the stages of the buyer journey: Awareness, Consideration, Decision, Delight.

I have written about 300 answers just through Clarity which have helped me generate many clients for www.Unthink.me - this is an example of targeted / strategic content marketing.
--> https://clarity.fm/humbertovalle <-- go to bottom of page to Answers section.

I have also written an article here about what is inbound marketing and how it helps generate traffic and leads
--> http://blog.unthink.me/what-is-inbound-marketing-and-can-it-really-help-my-business
--> http://blog.unthink.me/

I hope this helps you understand the possibilities of what can be done to help you get sales. If you would please follow me on Twitter @HumbertoVee and or http://facebook.com/iwillUnthink

1. Who is your target customer?

2. Are they local, national, or international?

2. With a staff of list builders and researchers, have you tried prospecting to lists your team can assemble for you?

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Over the long-haul, being able to leverage content as a means for nurturing prospects to the point of becoming paying customers will be key in scaling your marketing machine.

In the short-term however, focus on the identifying prospects who are already on a rapid trajectory towards a purchase through active prospecting.

Active prospecting can be hard to scale but tools like LeadFuze, Quickmail.io, and/or Streak CRM can help keep you organized and efficient at little to no cost.

A WORD OF CAUTION: Contrary to popular belief the goal of sales prospecting is not to sell.

The goals of prospecting are to gain market insight, sales-qualify your pool of prospects, and to initiate a sales dialog with prospects who have given you their permission to sell.

When done properly not only can prospecting rapidly convert cold prospects into revenue, but it can also provide you with a tremendous amount of market knowledge as well as a segmented list of leads.

Together, an understanding of your market and a well segmented list provide a unbeatable combination for long-term success and scale-ability in content marketing.

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Still not sure where to start or afraid you'll come off as a sleazy salesperson while prospecting?

Here's a recent interview I gave on how sellers can overcome their fear of sales and prospecting: http://bit.ly/2o5kF9X