First of all, read the instructions on http://www.linuxhelp.net/guides/bashprompt/bashprompt-print.php to learn how to set up a "PS1=..." line for your ~/.bashrc file. As you may already know, if you wish to make changes for all bash sessions, you can add such a line to the bottom of that file, or you may simply type it into a bash prompt to enable the configuration temporarily.
I will use as an example the following format, generated with the help of the website provided above:
PS1="\[\033[0;31m\]Linux\[\033[1;37m\]Box \\w"
Rather than adding this to your ~/.bashrc file and therefore modifying the prompt style of all your terminals, you can simply make a copy of your .bashrc file and make the changes to that file; call it whatever you would like (I call mine .bashrcalt).
cdcp .bashrc .bashrcalt
Then, in the GNOME Terminal profile settings for the specific profile you would like to work with, go to the "Title and Command" tab, check the box that says "Run a custom command instead of my shell," choose "Exit the terminal when command exits" and, for the command to run, set the following:
bash --rcfile .bashrcalt
Now, load a GNOME Terminal session with your custom profile enabled. e.g.:
gnome-terminal --profile=the_name_of_your_profile_here
You should be viewing the bash prompt with the custom set up you configured.