Just to be clear, there are at least two disparate types of grassroots marketing. One is a science of appealing to low income consumers in emerging markets. The other is the more general of applying social media techniques to a well-defined niche market.
I am assuming you fall in the latter. The former is much more complicated and would deserve much more information in order to comment constructively.
You can learn a lot about grassroots marketing by googling it rather than reading books. There are many current articles - make sure you only search for recent posts and articles. There are also many examples of successful campaigns on the web - for example, google "grassroots marketing examples". You can easily scan through hundreds and find something that is close to your situation.
At any rate, grassroots marketing in this vein requires:
1. a well-defined and narrow targeted group,
2. that can be reached via a combination of social media channels, and,
3. that has an interest in being reached and interacting.
In a grassroots campaign, rather than simply reaching out, it is usually imperative that you are successful in getting interaction. Some grassroots campaigns have involved novel contests, questions or gaming that, while kept at a relatively low cost by rewarding relatively few people, go viral by virtue of their novelty.
Again, I advise you to google the subject to get specific ideas that seem applicable to your business.