I confess this is advice I have gathered from others, rather than something that has worked for me (I haven't tried it for a paid product site like yours). It will always be a lottery emailing busy bloggers, but you could get lucky!

Something I have had success with is emailing smaller blogs that I know often feed stories to the larger ones, and also blogs that have insatiable appetites for new stories. Regarding smaller blogs, something that worked very well for me is to contact first the international spinoffs of highly popular blogs, rather than the standard US one - often they get far fewer emails daily, and stories they write get picked up by the main site.

edit: One way to get bloggers' attention would be to just give them a copy of your app. Don't write as if you're just asking for a write-up. Write to tell them you think they could probably benefit from your product, and you'd like to give them a free copy. And that if they like it, here's your phone number / email for more information.