In order to get you into the auto-complete, we need to establish authority for the keyword phrase. The time that it takes can vary depending upon the competitiveness of the keyword phrase, but look for the keyword phrases to start showing up in Bing within 30-40 days, and Google 90+ or more days. Google is Google. Sometimes with them it can be quicker or it can take months and months more.   For our own keywords that we have (of course we use them too, we are not silly) we don’t even care about Google at all.  We are happy with just Bing because they spend 35% more than clients we get from Google! And there is so little competition currently it is amazing!