Hi
Adobe Business Catalyst is a hosted CMS. That means you need to host in ADOBES datacentre for the CMS to work.
But that's not all bad news because Adobe apply the updates for you so you're always running the latest software. AND the SSL certficates / DNS hosting etc etc etc is all included in your website.
The Business Catalyst is designed so website owners are connected with a partner. The partner helps to ensure you've got someone to lead on for support, or when something falls over. It's highly recommended to have access to a good partner. Sounds like you ended up with a dud.
So to answer your question directly. No, you can't just transfer your site to another hosting company.
BUT - you can transfer your site away from your existing Partner to someone else.
If you're in Australia I can offer you a really attractive wholesale solution with no costs to you and will help you transfer free of charge.
I can also offer you Business Catalyst training if you need this.
Let me know if you need help getting this all sorted
Brett Stockley
02 9212 4485