I really can't recommend strongly enough that you read the wiki I linked.
DoF is an interaction between 4 primary factors:
Image plane size (ie sensor format, film format, etc).
Focal Length of the lens.
The f-stop at which you are shooting.
Distance from focal plane to image subject.
At a 1/3" sensor size, changes in f-stop are not going to alter your DoF considerably.
You MIGHT be able to go to the long end of the lens, wide open (lowest f-stop) and get a somewhat shallow field. Of course then you are very limited in camera placement because you need to move back in order to get the frame you want. There is a problem with that approach:
DoF INCREASES as you move farther from the lens. Changes in distance from lens to subject will change DoF FASTER than changes in focal length. Therefore even when you "zoom all the way in" you have to move back farther, which cancels out some of your approach towards a shallow DoF. This also means that you have to create artificial separation between the subject and their background which cannot always be done at location.
There's no need to buy them. Look around for someone with an adapter and a lens kit that might cut you a break for a student rental. You might even land one in trade for some favor or service, or even just for free.
Test it out. Find a frame you like with the lens zoomed all the way in and wide open and see if it is as shallow as you want. My gut feeling though is that A: it won't be quite what you seek, and B: the framing and camera placement will be very very limiting and make your shoot more difficult.
Voila! Shallow depth of field. The farther away your camera is from your subject and your subject is from the background, the shallower the depth of field.
I'm sorry, but that is only partially true. The distance in your equation is just a side effect to get the frame you need at the long end of the lens. Additionally, being able to physically separate the subject from the background is not always practical on the day. It's not a big deal to recommend people do this, but it should come with a caveat because it leads some people to understand the relationship between subject distance and DoF in reverse. I can't seem to repeat this enough around here: DoF INCREASES when the subject is farther from the lens and DECREASES when the subject is closer. It's a mathematical certainty.
The need to compensate by placing the subject farther from their background demonstrates this.
Sorry for being a stickler on this, but there's some fundamental science here that I think anyone asking this question should at least attempt to understand at a basic level before trying to "trick" things into place.