Rene, welcome to WebmasterWorld. Sorry for some initial abrupt comments you received (which have been removed). As you've probably discovered, we don't allow specifics on personal sites we discuss.
I believe I briefly saw the page at the url you posted before it was snipped and published. Didn't have time at that moment to deal with the post... and we don't give individual public site reviews in any case... but as I remember from a relatively quick glance, you didn't have any text content to speak of on your home page.
Google and Bing are similar in some ways, but they differe in others... and I've noticed that, depending on a page's backlinks and other confirming signals, Google often won't index a page with no text content. In truth, I haven't looked at Bing deeply enough to comment on that, but apparently they have indexed your page.
The main difference that I have noticed is that Bing is immensely kind to exact match and partial match domains, almost to the point of being ridiculous about it. I've seen domains which, because of weak or dupe content, receive absolutely no ranking in Google, but rank #1 in Bing on very competitive terms.
I've also felt that Google is much fussier about the quality of its inbound links, particularly with regard to relevance, whereas Bing is concerned more with the number of links. This may not apply in your situation, but it has applied in situations I've noted. And it may no longer be a fair assessment, as I haven't checked the difference that often.
When you say "noindexed" in Google, that can be a vague statement subject to many different interpretations....
- Does it rank for unique text strings on its page (difficult, if there are no text strings)?
- Does it rank for example.com (the domain name and TLD of your site)? If not, it's possibly been penalized?
- Or,does it simply not rank competitively for terms in Google you hope it will rank on? That's another situation entirely... not necessariy a penalty at all, but perhaps not good SEO, at least for Google. There are many factors to ask about.
- How old is the site? These days, ranking in Google can take time.
- How competitive are your targeted search terms?
- How long has the site been up?
- How old are the backlinks?
How were the backlinks obtained? Did you have control over their placement? Did you influence choice of anchor text? How would characterize what your inbound anchor text is like? How relevant are the linking pages? Etc....
This thread from a couple of years back, while not exactly on the subject of indexing, does discuss differences between Bing and Google enough perhaps to get some thoughts flowing. Check this thread and threads it links to... Poor ranking in Google but fantastic on Bing Nov, 2013 http://www.webmasterworld.com/google/4624483.htm
Please give us a better idea of what you mean by "indexed".