The UBB itself, along with just about any other php script that generates content from a database and is not primarily static content, may have extreme performance issues with Cloud Hosting environments.
With a database that large (really, anything over a 600mb database) I'd recommend you be at least on a VPS or Dedicated Server; especially if you're coming from a Pro Shared Hosting account. You're definitely looking at needing dedicated resources; and
BlueHost already provides some great solutions for VPS services.