I think the best approach is to figure out what's in it for the blogger. Some people are motivated by sharing their thoughts on cool new products or trends. Others are writing for a specific audience and are expecting a certain kind of content.
The other important point to keep in mind is that likely, these people are receiving a lot of emails a day - so how can you stand out? I try to keep my social media profile images consistent (those in email/Twitter/LinkedIn) and develop a relationship on one of these channels so they know who I am when I message them (or I remind them).
I put together some tips, which might be helpful:
http://www.crowdcrux.com/pitching-a-rep ... -campaign/