I have had similar experiences, with Google indexing a website within a week or so at the absolute most, and then as time passes and I check the rank tracking tool I use and begin to work on my SEO strat for the ascent up through the ranks of Google's SERPs. I start wondering why Yahoo and Bing do not appear to have any of my sites pages indexed and I begin to wonder what error I might have made, or perhaps I accidently did something agaist Yahoo / Bing terms of service and am blacklisted... It doesn't really bother me too much though since with the bulk of the market share, I'm pretty content to be in the good graces of Big G.
Usually, by the time my first round of SEO modifications starts to increase my rankings on Google, I start to show up on Yahoo and then a while later I will start to show up on Bing.
Bing's Webmaster Tools is similar to GWTs, and in my opinion BWT is much more useful. I would highly recommend that you register an account with Bing and take advantage of their excellent tools and would assume that you will start to see rankings with Bing much sooner from it's use as well.
