It would be best to connect some scraper to bubble whom replicates the blog content, but if you would want to go proxy, here you go.
Actually it wouldnt be a reverse proxy, just a proxy, but lets call it reverse for now as people mix names.
This would be potentially complex and has many pitfalls, but if you wanna test the waters here you go.
Get yourself a nginx reverse proxy server. Digitalocean is a good alternative, but should be located few hopes from your bubble server location. Read an article about how to setup "nginx reverse proxy" Digitalocean has some good blog posts about that.
Then you create an nginx config that proxies to your bubble install, (It its SSL/HTTPS you need to also forward HTTPS requests, so likely you would need a Letsencrypt certificate (google how to setup that).
Then you add a location directive in NGINX config that points your subdirectory to your other server,
Sorry for such a simplified writeup, but this is complex waters and not recommended for noobs. Your application may break at any time and you should have a mitigation strategy/24h response person if your app is mission critical.
Disclaimer: All your traffic would now go through this endpoint.