How could I measure the colour spectrum of a light bulb and investigate how closely it matches a black body radiation curve? Here is my research question: 
What is the colour/spectrum produced by each globe type?  What is the temperature equivalence? How closely does a globe match a black body radiation curve?
I will be testing this on halogen, compact fluorescent, and LED bulbs. How could I measure the colour specturm of the bulb? I have been suggested to take photos of the glowing bulb then use photoshop to analyse the colour. Is that a possible solution?
How could I match it to a black body radiation curve? Would I have to plot it out? From research it doesn't seem like a curve that could be hand-drawn, especially CFL and LED: 
 A: 
I have been suggested to take photos of the glowing bulb then use photoshop to analyse the colour. Is that a possible solution?

No.  The power spectrum of a light bulb is a continuous function $f(\lambda)$ where $\lambda$ is a particular wavelength of light and $f(\lambda)$ is the intensity of the light at just that one wavelength.
A camera throws most of that information away, and reduces a color to just three numbers.  That's because your eyes have just three different "color receptors," and almost every color that you are able to distinguish can be mimicked by combining different levels of a red, a green, and a blue light source.  The camera, therefore, records the level of light coming through a red filter, a green filter, and a blue filter at every pixel position.

Instead of directly photographing your different light bulbs, you could try photographing them through an inexpensive spectroscope
A: You will need to use a spectrometer to measure the irradiance at various wavelengths. A camera will only measure three wavebands (R/G/B) so this will not give you the necessary resolution to make a meaningful comparison of spectral composition.
A: If you need to do the experiment yourself,  and you dso not have a spectrometer available, you can make a crude spectrometer using a diffeaction grating and a cylindrical lens.  Make a thin slit in a piece of black paper, and let some of the light from your bulb pass through the slit.  Put the diffraction grating against the slit.  Downstream from the slit and grating, place the cylindrical lens.  Adjust the position and orientation of the lens and grating until you get a focused rainbow "needle"  on a piece of white paper further downstream.  Use a photographic light meter to measure the intensity of the light at every position in the rainbow.  This will give you a pretty good approximate spectrum of the light from the bulb.  Compare the spectra from your various sources.
You can buy a grating and a lens from Edmund Optics, for example.  You can use cello tape to hold the components in place on cardboard mounts.  Have fun!
