I made some test, I did not find the way to show the share count from VK unless use the default VK api. But the default vk api UI is different of Bee’s. It looks ugly.
There is the no-showing-count VK share-button guide(base on Bee 1.4.2):
1) Download the zip file and unzip it
style.css in bee folder
custom.pagebuild.js and custom.theme.js in bee/js folder
functions-view-module.php in bee/functions folder
post-social.php in bee/template folder