I may be able to provide a little insight into Bluehost, (although I do not work for them, and can only speak from personal experience).
If you are on the standard "dedicated" hosting, you shouldn't have a problem with cpu usage, although I do not know if they place a cap on the amount of traffic running to/from the dedicated server. It is very possible that they do this, and I would check with them directly.
A 5gig backup is pretty big, and yes, you should be doing incremental backups, rather than full. I am assuming this is a Linux-based server?
Since you have full access to a dedicated server, I would actually suggest you get someone to write you a script that does an incremental backup through CRON. That most likely will be the best thing for you. I do not know if there are other backup plugins that will do it, but with a dedicated server, you can do your own, a script will allow you to backup whenever you want it scheduled, at a specific time of night, make the backups redundant, (daily, weekly, monthly, etc). I think that is your best option.