What you need is shell access. According to their features page at http://www.bluehost.com/cgi/info/hosting_features, they support shell access via SecureShell (SSH). This is fairly common.
Download an SSH client like PutTTY and connect to yourdomain.com, or if you are on a Mac, open the Terminal app and type "ssh yourdomain.com" (with your web site's domain name). You can then run commands.
However, this probably will not get you what you need. You mentioned yum and rpm commands, which are system-level software installation tools. You'll need root access to do that, which you certainly cannot do on a shared hosting account.
These types of tools are really intended for application service providers. I'm fairly familiar with New Relic's products. I'm guessing you are trying to install the server monitor tool. You probably don't need to worry about that one since Bluehost should be monitoring their servers for you.