Every site I have ever submitted to Google/Bing have shown up within a week. But it depends on the search. We showed up in really niche specific searches in a few days but it took three months for us to show up in more general searches. Google knows about your page pretty soon after you submit it to them, but they aren't going to show you in a search until they find enough value in your site for that particular search.

What were you searching to find your site?