Jon pulled his catalogue from ASCAP a few years ago. He's listed with Azoff's Global Music Rights now. I think the only songs of his that are still listed on ASCAP are the ones he co-wrote with another ASCAP writer.

You might find something here.

https://globalmusicrights.com/search

I searched on "Jon Bon Jovi" and it showed 1-25 of 386 results; but when I clicked "Show More" it took me to the dialpad on my phone, so you may have to call or register for the full list. I tried searching by title but it returned zero results.