When asking prominent bloggers for links, it's best to have a clear goal of what kind of link you want. Are you pushing for a mention of your site in a post, a simple comment link, or to be added to their blog roll? And for best results, try not "asking" for the link outright, instead, becoming familiar with the blogger by commenting on a post or two, building up a rapport, and then eventually submitting your content in a question (be it an article, a new video, or even your own blog post) as link fodder.
As for highly authoritative sites, the process is a bit more complicated. First, you'll have to establish yourself as some sort of trusted resource that they can direct their audience to. Again, it's best to not ask for links off the bat. Instead, try asking if you can use them as an expert source for future content, and let them know you're including a link to their published work or Web site for your customers.