I've been using bluetooth to transfer applications when I was in high school, using a low-end smart phone that can't smoothly run numerous softwares like ShareIt. The first thing you have to do is locate the .apk file of the application you want to send or share. If you're not familiar with an .apk file, it looks like this in your File Manager or Storage/File Viewer
A lot of File Manager apps organize your files making it easier to locate. For instance, ASUS' default File Manager has it directly accessible in the home page
If there's not feature organizing your files in your File Manager, you can manually find the file by searching on the search box. Just type ".apk" and click "search". On the results, find the file with the name of the app you're trying to find or anything related to it (because some apps' apk files doesn't have the same file name as the app itself).
When you successfully located the .apk file, just long press and find a "share" or "send" option. After that, click "send to bluetooth" or "bluetooth". From here, it will be easy just like sending any other file. Just pair if you haven't paired with the device you're trying to send or just click its device name and you're good to go.
On the last note though, if you can't find your .apk file, it's possible that you didn't turn on "save apk upon installing" option when you installed the app especially when you got it from Play Store. If this is the case, there's no way you can send the app using bluetooth making your ShareIt as your last resort.
Hope this helps.