There's no 100% correct answer and I don't think someone from Microsoft could even give you an exact timeframe. Depending on factors such as inbound links, domain aging, code validity, server setup, etc it could be anywhere from a day to over a month. Remember, it's not just that they can find you, but also that the crawler has available process time to crawl your site.
In my experience, if I've got the domain parked with some "shell" content and roll the new site over, it's generally picked up in 3-4 days. I have had a site languish nearly a month without getting picked up for whatever reason. But in that case I registered a fresh domain immediately before launch, paid little attention to linking, and had a site with some undoubtedly obscure content that I doubt more than a few people were searching for at first....but the work paid the bills, so I guess I couldn't complain. Ironically, that same site now gets ridiculous traffic thanks to some very positive non-web PR. Go figure.
Good luck, be patient. It sounds like you've taken steps to make this process go well, so I'm sure you'll see your site on Bing soon.