bit.ly url shortener for sharing generates link for images

Try clearing the bitly cache from the Miscellaneous section at the plugin configuration page in the admin area.
Can you enable social share icons at the problematic web page and post the link?

I cleared the bitly cache and will observe.

Here’s a page where the image of “facebook group” generated a bitly: https://sonnylabayna.com/

Currently, share icons are sharing the URL of the home page of your website and the image appearing in the sharer is the one used by the og:image meta tag in the HTML source of your web page. It works like this. Let me know if I missed anything.