Corresponding BV Value to a Hertzsprung–Russell I have an example BV value from an astronomical catalog of 1.04 (33 Psc, HD Catalog 28).

Given only the number 1.04, can that be charted on the HR, or do I need the individual components of the value and/or temperature and luminosity?

Edit:

I should explain why I'm asking. I've written an application that displays data from one of several catalogs, and they only provide the BV value. I want to add a component to the application that would show an HR diagram with that star superimposed on it. The example of 33 Psc was semi-random, as it's the third entry in one of the catalogs (Yale Bright Star Catalog).
The HR diagram is a plot of luminosity (or a proxy) versus temperature (or a proxy).

$B-V$ is a proxy related to temperature, therefore to plot your point on a 2-d plot you obviously need the other axis information - the luminosity, or its proxy the absolute magnitude. This in turn needs an apparent magnitude and a distance to the star.

It is also possible that the star has suffered some extinction and reddening by the interstellar medium, which would need to be estimated and corrected for before comparing with other stars or stellar models.

Note however that 33 Psc is a binary star, so it isn't clear what you learn by plotting its combined colour and absolute magnitude on the HR diagram.

Edit: I note that the catalogue you show in your edited question doesn't just give $B-V$, it gives the visual (i.e. $V$) magnitude. This is one component of what you need for the y-axis. The other is a distance, so that you can convert your apparent $V$ magnitude into an absolute magnitude.