Help! My site is blocked by Bing. How to get out of Bing jail?

I hope someone has been in this situation and knows how to help.

Recently I decided to check on my Bing indexing and was unpleasantly surprised.

I registered with Bing, verified my site, submitted a site map and Fetched posts. Tried to look at index results and keywords - nothing, zero, nada.

After several attempts to resubmit the sitemap or verify again I googled a bit about it.

Found out that Bing might be actively blocking me and that it can be because of some false positive test done by their bot.

I wrote to their support and after couple of days got the following:

I was kind of shocked. My website is in a great relationship with Google (the peak day last Monday was 14K page views, all from organic traffic), I run Google AdSense, I'm Amazon associate, no issues whatsoever. Why Bing is blocking me?

As I'm technically challenged to read their guides, I decided to contact our Site Support team here. They checked and told me that the problem is with the pop-up ads I have on my website.

Here is their reply:

I insert AdSense units in my posts manually, where I need a break in the text wall. In addition to AdSense I use another network, that provides tiny slide-in ads on the bottom of each page.

I can't say that Support is wrong, but I'm not sure this is the right answer as well. If I was indexed before ads and then removed, that would be reasonable explanation.
Actually, I don't think I was EVER indexed by Bing, not even before I've started using ads.

That's why I really feel lost here. Google is the major engine and it "likes" me, so I'm not in too bad situation. But Bing has its share that I'm sad to lose.

Any experience you have to share about Bing, deindexing, ads etc?

Thank you in advance

Mary